Решение задач из учебника Ю.Н. Макарычева, Н.Г. Миндюк, К. И. Нешкова, С.Б. Суворовой «Алгебра. 7 класс»

y = kx + b an . ak = an +k an : ak = an -k Решение задач (a n)k = a nk (a - b)(a + b) = a 2 - b 2 Из учебника Ю. Н...

Author: сост. Н.Д. Луканов

7 downloads 166 Views 7MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!

Report copyright / DMCA form

DOWNLOAD PDF

y = kx + b an . ak = an

+k

an : ak = an

-k

Решение задач

(a n)k = a nk (a - b)(a + b) = a 2 - b 2

Из учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой

«Алгебра. 7 класс»

(a - b) 2 = a 2 - 2ab + b 2

(М.: Просвещение, 2004)

(a + b) 2 = a 2 + 2ab + b 2 a 3 + b 3 = (a + b)(a 2 - ab + b 2) y = kx + b an . ak = an

+k

an : ak = an

-k

(a n)k = a nk (a - b)(a + b) = a 2 - b 2

Москва ОНИКС Мир и Образование 2005

УДК 512(076.2) ББК 22.14 Р47

Автор-составитель Н. Д. Луканов

Решение задач из учебника Ю. Н. Макарычева, Н. Г. МинР47 дюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс» / Авт.-сост. Н. Д. Луканов. — М.: ООО «Издательство Оникс»: ООО «Издательство «Мир и Образование», 2005. — 288 с.: ил. ISBN 5-488-00120-4 (ООО «Издательство Оникс») ISBN 5-94666-237-6 (ООО «Издательство «Мир и Образование»)

Пособие содержит решения всех задач из последнего издания учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс», включая и задач и повышенной трудности. Оно будет полезно ученикам и их родителям при проверке домашних заданий и незаменимо в тех случаях, если ученику приходится заниматься самостоятельно. УДК 512(076.2) ББК 22.14 ISBN 5-488-00120-4 (ООО «Издательство Оникс») ISBN 5-94666-237-6 (ООО «Издательство «Мир и Образование») © ООО «Издательство «Мир и Образование», 2005 © Оформление обложки. ООО «Издательство Оникс», 2005

Ãëàâà I ÂÛÐÀÆÅÍÈß, ÒÎÆÄÅÑÒÂÀ, ÓÐÀÂÍÅÍÈß

§ 1. Âûðàæåíèÿ 1. ×èñëîâûå âûðàæåíèÿ

---

2

3

–

– - ------ --------------------------- ------------ ------ ----

+ + - ------------ --- --- --- --- --------------------------

- --- ------ ---------------- ------ --- ----

------ --- ------------------- --- --- --- ---

------ ------ ------ ------ -------------------

--- ---

------ -------------------- ---

------ --- ------------------- --- ---

---

--- ---

+ ------ ------ --- --- –---------------------

– --- --- ------------ ------ ------

- ------------------- --- --- ----

- ---

--- --- ---------------

--- --- --- ---

4

– – - ------------------ ------ --- --- --------------------------

+ + - --------------- ------ ------ --- --- --------------------------

------ ------ ------ ---

------ ------ --- --- --- ---

+ + - ------------------- ------ ------ --- --- ---------------------------

5

–

– - ------ --------------------------- ------------ ------ ----

+ + - ------------ --- --- --- --- --------------------------

- --- ------ ---------------- ------ --- ----

------ --- ------------------- --- --- --- ---

------ ------ ------ ------ -------------------

--- ---

------ -------------------- ---

------ --- ------------------- --- ---

---

--- ---

+ ------ ------ --- --- –---------------------

– --- --- ------------ ------ ------

- ------------------- --- --- ----

- ---

--- --- ---------------

--- --- --- ---

4

– – - ------------------ ------ --- --- --------------------------

+ + - --------------- ------ ------ --- --- --------------------------

------ ------ ------ ---

------ ------ --- --- --- ---

+ + - ------------------- ------ ------ --- --- ---------------------------

5

- ------------- --- --- ----

6

------ ------------------ --- --- --- ---

--- ---

--- --- --- --- ---

- --- --- --- --- ----

------ ------------------- --- --- --- --- ---

- --- --- --- --- ------------

--- --- --- --- ---

- --- --- --- ------------

- ------ ------ ------ ---------------------- --- --- --- ----

--- --- --- --- ---

+ - ------ --- --- ----------

- --- --- --- ----

– - --- --- --- -----------

+

+ - --------------- ------ --- --- ------------------

- --- --- --- ------ -----

- --- --- --- ------------------- ------ --- --- --- ---------------

--- --- --- ---

---------------- ------ --- --- ---

- --- --- ------ ------ -----

------ --- --- ---

------ --- --- --- --- --- ---------

- --- --- -------------------------

- --- --------------------------------- --- --- ----

+ ------------------- ------ ------ ------ --- ---

–+ --- --- --- -------------------- ---

+– --- --- --- --------------------

--- ---

- --- --- -------------

------ ------ -------------------- --- --- --- ---

- --- --------------

- --- --- --- --- -----

–+ - --------------------- --- ------- ------- ------

--- ---------------

------ --- --- ---------------

------ --- ------------------- --- --- --- ---

--- --- --- ---

------ ---------------- --- --- --- ---

7

– - ------ --- --- ----------

- ------------- --- --- ----

6

------ ------------------ --- --- --- ---

--- ---

--- --- --- --- ---

- --- --- --- --- ----

------ ------------------- --- --- --- --- ---

- --- --- --- --- ------------

--- --- --- --- ---

- --- --- --- ------------

- ------ ------ ------ ---------------------- --- --- --- ----

--- --- --- --- ---

+ - ------ --- --- ----------

- --- --- --- ----

– - --- --- --- -----------

+

+ - --------------- ------ --- --- ------------------

- --- --- --- ------ -----

- --- --- --- ------------------- ------ --- --- --- ---------------

--- --- --- ---

---------------- ------ --- --- ---

- --- --- ------ ------ -----

------ --- --- ---

------ --- --- --- --- --- ---------

- --- --- -------------------------

- --- --------------------------------- --- --- ----

+ ------------------- ------ ------ ------ --- ---

–+ --- --- --- -------------------- ---

+– --- --- --- --------------------

--- ---

- --- --- -------------

------ ------ -------------------- --- --- --- ---

- --- --------------

- --- --- --- --- -----

–+ - --------------------- --- ------- ------- ------

--- ---------------

------ --- --- ---------------

------ --- ------------------- --- --- --- ---

--- --- --- ---

------ ---------------- --- --- --- ---

7

– - ------ --- --- ----------

-------------------- 02'33'"

--- --- --- --- ---

-------------------- 02'3'"

--- --- --- ---

--- --- --- --- ---- ----

--------- --- --- --- --- --- ---

-#$'"4##5'

"0-7(%#45%$ %

!"#$! % &!'%( % )!#' % *%''$ % +, % +,-!#'$ % *%''$!'%' %

&!'%( % %,. % )!#' % %'"'$ ' *%''$%,. %'

/ 01

/ 01 / 01 / 01

------------------

- --------------------------

---------------------------------

---------------------------------

8

-#.5%#%-6(4'"

-------------------- 2 0'%((4%%(% "

2 %"%%(

2-4'2.

2. Âûðàæåíèÿ ñ ïåðåìåííûìè 8% % % 8% % %

- --------------------

"

- " 0#%-633% ------------------------

- "0#%-63% ---------------------

9

-------------------- 02'33'"

--- --- --- --- ---

-------------------- 02'3'"

--- --- --- ---

--- --- --- --- ---- ----

--------- --- --- --- --- --- ---

-#$'"4##5'

"0-7(%#45%$ %

!"#$! % &!'%( % )!#' % *%''$ % +, % +,-!#'$ % *%''$!'%' %

&!'%( % %,. % )!#' % %'"'$ ' *%''$%,. %'

/ 01

/ 01 / 01 / 01

------------------

- --------------------------

---------------------------------

---------------------------------

8

-#.5%#%-6(4'"

-------------------- 2 0'%((4%%(% "

2 %"%%(

2-4'2.

2. Âûðàæåíèÿ ñ ïåðåìåííûìè 8% % % 8% % %

- --------------------

"

- " 0#%-633% ------------------------

- "0#%-63% ---------------------

9

+#%#''. !' '$ ''.6 #.9'5 $#$:%$ -#-9'. %

--- ---

--- ---

--- --- --- ---

8%

--- ---

10

- ------- ------ ------ --- ---------- –

– - ----------- ---------- –

–

--- --- ---

---

--- 2 0%%-#", % !"#$

% "&"#$ '% "&"#$ ()*+ %( #'%5 ''%5 #

11

+#%#''. !' '$ ''.6 #.9'5 $#$:%$ -#-9'. %

--- ---

--- ---

--- --- --- ---

8%

--- ---

10

- ------- ------ ------ --- ---------- –

– - ----------- ---------- –

–

--- --- ---

---

--- 2 0%%-#", % !"#$

% "&"#$ '% "&"#$ ()*+ %( #'%5 ''%5 #

11

d

S1

S2

c

d

b–c

S3 a

n

---

- --------------------------

---------------------------

a )7(-$,"(' ,-(.-"!/*$ ),-%,#,6! '.6%' ;#''$' %%('4#% %%(65'"'4 %%(#,656'45

)!#' 01*/ +, %-!#'$ % )!#'%,. % % &!'%( %-!#'$ % +,-!#'$ % %

12

'-

--- 0'4'2'.2''4

)#%6 ,2- ,

'-

h

m

S2 S1 y

)#%6 , &$-

,

x

x–y

+, %'" % % +,-!#'5'' )!#'!'% % '%,, %

b

- --------------------------

----------------------------

/// 0%(-2'#-< 6%$'

- --------------------------

. / / / 0-6%$'%'#

- % ------------------------

--',!#9'.#.-,%(%'#

3. Ñðàâíåíèå çíà÷åíèé âûðàæåíèé = = =

13

d

S1

S2

c

d

b–c

S3 a

n

---

- --------------------------

---------------------------

a )7(-$,"(' ,-(.-"!/*$ ),-%,#,6! '.6%' ;#''$' %%('4#% %%(65'"'4 %%(#,656'45

)!#' 01*/ +, %-!#'$ % )!#'%,. % % &!'%( %-!#'$ % +,-!#'$ % %

12

'-

--- 0'4'2'.2''4

)#%6 ,2- ,

'-

h

m

S2 S1 y

)#%6 , &$-

,

x

x–y

+, %'" % % +,-!#'5'' )!#'!'% % '%,, %

b

- --------------------------

----------------------------

/// 0%(-2'#-< 6%$'

- --------------------------

. / / / 0-6%$'%'#

- % ------------------------

--',!#9'.#.-,%(%'#

3. Ñðàâíåíèå çíà÷åíèé âûðàæåíèé = = =

13

+ - ------ --- --- --------------------------

+ --- --- ---------------------------- ------

------ = ------ -1, --- --- = --- ---

--- --- --- --- --- --- --- --- ---

--- > --- --- > --- -1, --- > ---

- --- ---------------- --- --------------

-1, --- ---

= – – - ------------------ ------ --- --- -------------------------

--- --- ---------- ------

------ ------

--------- ---------

--------- = --------- -1, --------- > --------- --- --- > --- ---

–

---------- -------- ------------------------------ ------

– - ------ --- --- -------------------------

------ = ------ -1, --- --- = --- ------

--- --- --- = --- ---

- ------ --- --- --- --- --- --- --- -----------

– - --- --- --- --- --- -------------------------

--- --- ---

= ---

?#'%##'

> > ?#'%##' >-1, >

14

+– - -------- -------- --------------------- --- --- ------ - --- --- --- ----

--- = ------ -1, --- --- --- = --- --- ---

) = -1,- = ) = -1,- = ) = -1,- = ) -1,- ) =-1,- = ) = -1,- = ) = -1, = - ) -1, - ) > -1, > - ) > -1, > - ) -1, - ) = -1, = - ) > -1, > - ) -1, - ) = -1, = - ) > -1, > -

15

+ - ------ --- --- --------------------------

+ --- --- ---------------------------- ------

------ = ------ -1, --- --- = --- ---

--- --- --- --- --- --- --- --- ---

--- > --- --- > --- -1, --- > ---

- --- ---------------- --- --------------

-1, --- ---

= – – - ------------------ ------ --- --- -------------------------

--- --- ---------- ------

------ ------

--------- ---------

--------- = --------- -1, --------- > --------- --- --- > --- ---

–

---------- -------- ------------------------------ ------

– - ------ --- --- -------------------------

------ = ------ -1, --- --- = --- ------

--- --- --- = --- ---

- ------ --- --- --- --- --- --- --- -----------

– - --- --- --- --- --- -------------------------

--- --- ---

= ---

?#'%##'

> > ?#'%##' >-1, >

14

+– - -------- -------- --------------------- --- --- ------ - --- --- --- ----

--- = ------ -1, --- --- --- = --- --- ---

) = -1,- = ) = -1,- = ) = -1,- = ) -1,- ) =-1,- = ) = -1,- = ) = -1, = - ) -1, - ) > -1, > - ) > -1, > - ) -1, - ) = -1, = - ) > -1, > - ) -1, - ) = -1, = - ) > -1, > -

15

) -1, - ) > -1, > - ) = -1, = - ) > -1, > - ) = ?#'%#'#' ) ?#'%#'#' ) > ?#'%##' (4 ''(4 (4 ''(4 (4 ''(4 (4''(4 (4 --- ''(4 ---

--- (4''(4

> > > > >> > > > > > ?- - --- ------ --- ----

?- -------

------ ?-

------ --------- ------ ---------

--- > -------> ---

?-

- ------ --- -----

> >

> >

--- ------ ------

--- > ------ > ---

16

> > > =

> --- >

>>

>> > >

=

b b
a

c

x

'(4#' (4#' (4#' '(4#' (4#'''(4#' (4#'''(4#'

(4#' ''(4#' (4#' ''(4#' ) > 0#' - 0#' - > 0'#' ) = 0'#' - 0#' - = 0#' ) 0'#' - 0'#' - 0#' - 0#' - 0'#' ) 0#' - 0#' - 0#' - 0#' - 0'#'

>

=

> 33

>

>

17

> !

) -1, - ) > -1, > - ) = -1, = - ) > -1, > - ) = ?#'%#'#' ) ?#'%#'#' ) > ?#'%##' (4 ''(4 (4 ''(4 (4 ''(4 (4''(4 (4 --- ''(4 ---

--- (4''(4

> > > > >> > > > > > ?- - --- ------ --- ----

?- -------

------ ?-

------ --------- ------ ---------

--- > -------> ---

?-

- ------ --- -----

> >

> >

--- ------ ------

--- > ------ > ---

16

> > > =

> --- >

>>

>> > >

=

b b
a

c

x

'(4#' (4#' (4#' '(4#' (4#'''(4#' (4#'''(4#'

(4#' ''(4#' (4#' ''(4#' ) > 0#' - 0#' - > 0'#' ) = 0'#' - 0#' - = 0#' ) 0'#' - 0'#' - 0#' - 0#' - 0'#' ) 0#' - 0#' - 0#' - 0#' - 0'#'

>

=

> 33

>

>

17

> !

--------- @ 0%'$$%%(#$AB",C

--------- @ 0%'$$%%(#$AD%# C

@ @ > +'$$%%(#$AB",C'(4 @ @ = +'$$%%(#$AB",C(4

§ 2. Ïðåîáðàçîâàíèå âûðàæåíèé

-------------- / ---------------------------- / ----------- / --------- / /

----------- / ------------------------- / ------------------------------- //

------- / ---------------------------------- / /

-------/ --------------------//

------------ / ----------------------------- / /0%(-2'#

'2%%('' / / / %'2%%(' /

18

4. Ñâîéñòâà äåéñòâèé íàä ÷èñëàìè )%('%#5%#%9'$ )%('%#5%#,'9'$ + ('%#5%#%9'$ &%-('%#5%# + - -- --- --- ----------

-%('% ('%#5%#%9'$

19

--------- @ 0%'$$%%(#$AB",C

--------- @ 0%'$$%%(#$AD%# C

@ @ > +'$$%%(#$AB",C'(4 @ @ = +'$$%%(#$AB",C(4

§ 2. Ïðåîáðàçîâàíèå âûðàæåíèé

-------------- / ---------------------------- / ----------- / --------- / /

----------- / ------------------------- / ------------------------------- //

------- / ---------------------------------- / /

-------/ --------------------//

------------ / ----------------------------- / /0%(-2'#

'2%%('' / / / %'2%%(' /

18

4. Ñâîéñòâà äåéñòâèé íàä ÷èñëàìè )%('%#5%#%9'$ )%('%#5%#,'9'$ + ('%#5%#%9'$ &%-('%#5%# + - -- --- --- ----------

-%('% ('%#5%#%9'$

19

+ - --- -- --- --- ----------

-%('% ('%#5%#%9'$ --- --- --- --- --- --- --- ---

--- --- --- --- --- --- --- ---

%$ '#'45 ./-

-/ 4($"($ + ' ------------------------- @ 0%'$$%%(#$ & &+'

------ ------ ------ --- ------ ---

------ ------ --- --- ---

--- --- --- --- ---

--- --- ---

--- --- ---

- ------ --- --- ----

%$' %#('-!#'< %$' -1,''$%,!%$' %$ ' %#(' -!#' %$'-1,''$%,!%$'

20

------ 3 ------ 3 ------ (5-" --- 3 --- 3

" # $ %

B –2

D –1

C 0

A 1

2 x

%"# $

5. Òîæäåñòâà )%('%#5%#%9'$ + ('%#5%#%9'$ )%('%#5%#%9'$ &%-('%#5%# )%('%#5%#,'9'$ &%-('%#5%# )%('%#5%#,'9'$-%(' %#5%#%9'$ + ('%#5%#,'9'$ E#$:%$ E#$:%$ ?$#$:%$ E#$:%$ ? ? E &%-('%#5%# +,-#-9'.6 %#' -!#':" %#'

21

+ - --- -- --- --- ----------

-%('% ('%#5%#%9'$ --- --- --- --- --- --- --- ---

--- --- --- --- --- --- --- ---

%$ '#'45 ./-

-/ 4($"($ + ' ------------------------- @ 0%'$$%%(#$ & &+'

------ ------ ------ --- ------ ---

------ ------ --- --- ---

--- --- --- --- ---

--- --- ---

--- --- ---

- ------ --- --- ----

%$' %#('-!#'< %$' -1,''$%,!%$' %$ ' %#(' -!#' %$'-1,''$%,!%$'

20

------ 3 ------ 3 ------ (5-" --- 3 --- 3

" # $ %

B –2

D –1

C 0

A 1

2 x

%"# $

5. Òîæäåñòâà )%('%#5%#%9'$ + ('%#5%#%9'$ )%('%#5%#%9'$ &%-('%#5%# )%('%#5%#,'9'$ &%-('%#5%# )%('%#5%#,'9'$-%(' %#5%#%9'$ + ('%#5%#,'9'$ E#$:%$ E#$:%$ ?$#$:%$ E#$:%$ ? ? E &%-('%#5%# +,-#-9'.6 %#' -!#':" %#'

21

?- F6!' '5' E#$%$ ?$#$%$ E#$%$ ?$#$%$ E#$%$ E#$%$ E#$%$ ?$#$%$

- ---------------------------- --- --- ---------------------

--- ---

- ------ -------

- ------ ----

- --- ------------------- ------ ------ -----

- --------- ------ --- ----------------------------

! ! !

--- --- --- --- ---

) = -1, = ) > -1, > ) > -1, >

6. Òîæäåñòâåííûå ïðåîáðàçîâàíèÿ âûðàæåíèé

22

'('('(

' ' '

23

?- F6!' '5' E#$%$ ?$#$%$ E#$%$ ?$#$%$ E#$%$ E#$%$ E#$%$ ?$#$%$

- ---------------------------- --- --- ---------------------

--- ---

- ------ -------

- ------ ----

- --- ------------------- ------ ------ -----

- --------- ------ --- ----------------------------

! ! !

--- --- --- --- ---

) = -1, = ) > -1, > ) > -1, >

6. Òîæäåñòâåííûå ïðåîáðàçîâàíèÿ âûðàæåíèé

22

'('('(

' ' '

23

' ' ' - - - - ' '' ''

((((( - ( --- ---

- --- --- - ' ' ' '' -1, --- > ---

--- = ---

--- --- = --- --- >

---

!!!!! ''' '' - '

24

-1,

--- >-1,

--- --- = --- ---

--- >

--- > --- >

- / / 0 %( -2'# %'# ----------------------------------

%#.-,%( // / ' /-#.%%$#.-,%%'##%, A

–4

E

C

–2

F 0

BD 2

4 x

% " --- #$) --- *

25

' ' ' - - - - ' '' ''

((((( - ( --- ---

- --- --- - ' ' ' '' -1, --- > ---

--- = ---

--- --- = --- --- >

---

!!!!! ''' '' - '

24

-1,

--- >-1,

--- --- = --- ---

--- >

--- > --- >

- / / 0 %( -2'# %'# ----------------------------------

%#.-,%( // / ' /-#.%%$#.-,%%'##%, A

–4

E

C

–2

F 0

BD 2

4 x

% " --- #$) --- *

25

§ 3. Óðàâíåíèÿ ñ îäíîé ïåðåìåííîé 7. Óðàâíåíèå è åãî êîðíè ), #' %# #'%# -1, $#$%$ '''",#''$ *%##'%#'$#$%$#'.-1,'$#$< %$'''",#''$ '$#$%$',#''$ 0''(,#''$ 0''(,#''$ 0'(,#''$ 0''(,#''$ 0'(''",#''$ 0'(,#''$ 0''(,#''$ 0''(,#''$ 0'(,#''$ 0''(,#''$ 0'(,#''$ 0'(,#''$ 0''(,#''$ G'$''",#''$$#$:%$ %

26

) 9 ! !' '5 #$ %( ,#''$ < 7%$ # -!#' #' ',: % 6$ . ' ! '95 #' )1, 9 ! < % $#$%$'''",#''$ )9!!' '5,#''7%$##' %##'%# )1, $#$:%$'$ ,#''$ &#'%# #' - :.6 !' '$6 -''5 %< #(' 4' ''" ,#''$ $#$%$ : % &#'%#'#''-6!' '$6-''5-< 1,'',#''''5 &#'%#'#''-6!' '$6 %#(< ',#''''5 ;#''''( ?-

?-

;#'''$ ;#''''5

;#'''( ;#'''$

;#''$#'%('.:'9' ------

;#''$#'%('.:'9' ;#''$#'%('.:'9'

27

§ 3. Óðàâíåíèÿ ñ îäíîé ïåðåìåííîé 7. Óðàâíåíèå è åãî êîðíè ), #' %# #'%# -1, $#$%$ '''",#''$ *%##'%#'$#$%$#'.-1,'$#$< %$'''",#''$ '$#$%$',#''$ 0''(,#''$ 0''(,#''$ 0'(,#''$ 0''(,#''$ 0'(''",#''$ 0'(,#''$ 0''(,#''$ 0''(,#''$ 0'(,#''$ 0''(,#''$ 0'(,#''$ 0'(,#''$ 0''(,#''$ G'$''",#''$$#$:%$ %

26

) 9 ! !' '5 #$ %( ,#''$ < 7%$ # -!#' #' ',: % 6$ . ' ! '95 #' )1, 9 ! < % $#$%$'''",#''$ )9!!' '5,#''7%$##' %##'%# )1, $#$:%$'$ ,#''$ &#'%# #' - :.6 !' '$6 -''5 %< #(' 4' ''" ,#''$ $#$%$ : % &#'%#'#''-6!' '$6-''5-< 1,'',#''''5 &#'%#'#''-6!' '$6 %#(< ',#''''5 ;#''''( ?-

?-

;#'''$ ;#''''5

;#'''( ;#'''$

;#''$#'%('.:'9' ------

;#''$#'%('.:'9' ;#''$#'%('.:'9'

27

) - - % " # $ ) *

y E 1 F D 0

A

B

x

1

C

---

' --- '

--- --- ---

------ ---

---

---

--- --------- ---

28

- --- --- --- --------------

--- ---

--- ---

' --- ' --- '

------

---

---

8. Ëèíåéíîå óðàâíåíèå ñ îäíîé ïåðåìåííîé

--- ------ ------

--- --- --- --- --- --- --- ------- --- ---

--- ---

---

! --- !

--- ---

--- !

!

29

) - - % " # $ ) *

y E 1 F D 0

A

B

x

1

C

---

' --- '

--- --- ---

------ ---

---

---

--- --------- ---

28

- --- --- --- --------------

--- ---

--- ---

' --- ' --- '

------

---

---

8. Ëèíåéíîå óðàâíåíèå ñ îäíîé ïåðåìåííîé

--- ------ ------

--- --- --- --- --- --- --- ------- --- ---

--- ---

---

! --- !

--- ---

--- !

!

29

------

- -----

--- --- ---

--- --- ---

+ -------- -------- ------------ --- ---

--- ---

--- ---

---

------ --- --- --- --- ---

+ - -------- ------------ --- ' --- --- --- ' ' --- ' --- --- ------

--- ' --- ---

--- --- ------------ ---

' ---

--- --- --- ---

--- --- --------- --- ---

---

---

'' '' ' ' ' '

------

------ ------ ---

---

---

------ ------

G'5'

30

31

------

- -----

--- --- ---

--- --- ---

+ -------- -------- ------------ --- ---

--- ---

--- ---

---

------ --- --- --- --- ---

+ - -------- ------------ --- ' --- --- --- ' ' --- ' --- --- ------

--- ' --- ---

--- --- ------------ ---

' ---

--- --- --- ---

--- --- --------- --- ---

---

---

'' '' ' ' ' '

------

------ ------ ---

---

---

------ ------

G'5'

30

31

&#'%# #' - : !' ' ,#'' %' ''9%#4'5 G'5' G'5' G'5' : %

G'5'

32

--- --- ---

--- ---

---

--- ---

?- > > - ------ --- ------ ------ --- ----

- ?- ----

------ > ------ > ------

- > --- -1, --- > ----

?- >> ------ --- ------ ---

------ ?-

------ > ------ > ------

33

------ > --- -1, --- >

&#'%# #' - : !' ' ,#'' %' ''9%#4'5 G'5' G'5' G'5' : %

G'5'

32

--- --- ---

--- ---

---

--- ---

?- > > - ------ --- ------ ------ --- ----

- ?- ----

------ > ------ > ------

- > --- -1, --- > ----

?- >> ------ --- ------ ---

------ ?-

------ > ------ > ------

33

------ > --- -1, --- >

y

G %#:76

B

A 1 D

0 1

C

x

- -

),%( '(4$ %' % " 9$ ! #'.6 9, %5 %' #' % ) < ,"('#' % -,%#:! #' % +%#,#'' '(4$ %' #' % 9$ ! #,6,"60 % ),%(-#.5 5!"# 5"#5 0 5 H%"'!"# 5 -,%#:#' $ +%#,#'' !"#!"! 5

34

H%"

H%"#6266 # -,%#:!< #' +%#,#'' #-#26 ### ##( #

D%%"

9. Ðåøåíèå çàäà÷ ñ ïîìîùüþ óðàâíåíèé ),%(#33%%- #"#3%%-< # H%"- # -,%#:! #' +%#,#'' #33%%- #3%% #

326 3326 33326

+# J- JI

H%"

H%"!%6# " -,%#:#'

" +%#,#''

'4-,!%6# "4%'%#0 "'4I0 "

G'" 3- 33- 333-

H%"

H%"'6-6 '" -,%#:#' '" +%#,#'' ---

*% '" 9' .( #.9' ',('. % --- 0 %'',('

%-9''#!9'

35

y

G %#:76

B

A 1 D

0 1

C

x

- -

),%( '(4$ %' % " 9$ ! #'.6 9, %5 %' #' % ) < ,"('#' % -,%#:! #' % +%#,#'' '(4$ %' #' % 9$ ! #,6,"60 % ),%(-#.5 5!"# 5"#5 0 5 H%"'!"# 5 -,%#:#' $ +%#,#'' !"#!"! 5

34

H%"

H%"#6266 # -,%#:!< #' +%#,#'' #-#26 ### ##( #

D%%"

9. Ðåøåíèå çàäà÷ ñ ïîìîùüþ óðàâíåíèé ),%(#33%%- #"#3%%-< # H%"- # -,%#:! #' +%#,#'' #33%%- #3%% #

326 3326 33326

+# J- JI

H%"

H%"!%6# " -,%#:#'

" +%#,#''

'4-,!%6# "4%'%#0 "'4I0 "

G'" 3- 33- 333-

H%"

H%"'6-6 '" -,%#:#' '" +%#,#'' ---

*% '" 9' .( #.9' ',('. % --- 0 %'',('

%-9''#!9'

35

@ 0%%(#4' F -5''.5 -,( ' 9 %%# ,#'' %%(#4'#' @

*%' 3$7 33$7 333$7

H%"

H%" ' - ,%#: #' +%# ,#'' H-#$7 '## ' # ( ' !7'#!9'

K.

+

3, %

,%#

,%#

33, %

,%#

,%#

+

,@

&

)# '$

F -,( - ': 9 -# '$ %%#,#''

%%#''$%%(-6@

,@

&

+

34'

334'

36

3"

#

#

33"

#

#

K.

+

3"

#

#

33"

#

#

),%#::5%-#', +%#,#'' #-#5". #

) ':

+

H 3 " !%( ' # (4 +%# ,#'' ##5". #% ##-#5"% #

F ' , %6 ,%# % -#', %%# ,#''

'#, %.,%#'-#

,%#

K.

),%('%!-%' % "-#.5, '-,< #5 0 F!,(-#" #!(4!,(#"%%#,#'' '%!-%' %

K.

+

G!'

"

"

E7

"

"

H !' % #'" (4 ' " +%# ,#'' #!'. "#'"

37

@ 0%%(#4' F -5''.5 -,( ' 9 %%# ,#'' %%(#4'#' @

*%' 3$7 33$7 333$7

H%"

H%" ' - ,%#: #' +%# ,#'' H-#$7 '## ' # ( ' !7'#!9'

K.

+

3, %

,%#

,%#

33, %

,%#

,%#

+

,@

&

)# '$

F -,( - ': 9 -# '$ %%#,#''

%%#''$%%(-6@

,@

&

+

34'

334'

36

3"

#

#

33"

#

#

K.

+

3"

#

#

33"

#

#

),%#::5%-#', +%#,#'' #-#5". #

) ':

+

H 3 " !%( ' # (4 +%# ,#'' ##5". #% ##-#5"% #

F ' , %6 ,%# % -#', %%# ,#''

'#, %.,%#'-#

,%#

K.

),%('%!-%' % "-#.5, '-,< #5 0 F!,(-#" #!(4!,(#"%%#,#'' '%!-%' %

K.

+

G!'

"

"

E7

"

"

H !' % #'" (4 ' " +%# ,#'' #!'. "#'"

37

),%( %% -#" ,! " " %% #" "%%(" " D%%-#"(" ,!##%#!(4%%.#" +%# ,#'' %%-#",!0"%%#"0 "%%(",!0 " ),%( %%( # " . # F %#%(#%%#,#'' %%( ),%(!'"4#!$ ""!,""#!$ " H'4%%( "#," " F # 3 4 %%( %6 # ! (4 %%#,#''

L!34#!$"#'%%( " L!334 #!$"#'%%( " # ' 4 %%( " %6 # ,< " 0" F % % F "

" F #

# F $

$

y

0

1

x A

- --- --------------------------

- --- ---------------------

-

– - --- ------------ --- --- --- ------

- --- --- --------------- ----

------ ---------------- ------ --- --- --- --- ---

- --- ----

>

= – -- ---------------- > + --

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå I

- ------------------- --- --- ----

M

1

--- --- --- ---

Ê ïàðàãðàôó 1

y

A

------ -------------------- ------ ---

B

0 1

x N

38

C

B

%"

---

--- --- >

D 1

--- --- ---

- --- --- --- ----

39

),%( %% -#" ,! " " %% #" "%%(" " D%%-#"(" ,!##%#!(4%%.#" +%# ,#'' %%-#",!0"%%#"0 "%%(",!0 " ),%( %%( # " . # F %#%(#%%#,#'' %%( ),%(!'"4#!$ ""!,""#!$ " H'4%%( "#," " F # 3 4 %%( %6 # ! (4 %%#,#''

L!34#!$"#'%%( " L!334 #!$"#'%%( " # ' 4 %%( " %6 # ,< " 0" F % % F "

" F #

# F $

$

y

0

1

x A

- --- --------------------------

- --- ---------------------

-

– - --- ------------ --- --- --- ------

- --- --- --------------- ----

------ ---------------- ------ --- --- --- --- ---

- --- ----

>

= – -- ---------------- > + --

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå I

- ------------------- --- --- ----

M

1

--- --- --- ---

Ê ïàðàãðàôó 1

y

A

------ -------------------- ------ ---

B

0 1

x N

38

C

B

%"

---

--- --- >

D 1

--- --- ---

- --- --- --- ----

39

--- --- --- --- ---

- --- --------------------

--- --- --- ---

- ------ ----

--- ---

40

– --- --- --- – --- --- -------------------------------------------------------------------------- --- --- --- – --- + --

- --- --- --- --- --- --------------

--- ---

------ ------------------- --- --- --- ---

--- --- ---

– + - -------- -------- ---------------------------- ------ - --- --- --- --- . ------

--- ---- ----------------- / --- ----

0 ---

--- + --- – --- ---------------------------------------------------------

--- – --- ------ --

--- ---------------

- ------------------- ------ --- --- ----

- --- ---

--------- --- --------- ------ ---

------ ---------------- ------ --- ---

- --- -----

- ------------------- -----

- --- ----

- ------ --- -----

------ ------ ----------------- --- ---

+– - -------- -------- --------------------- ------ -------

------ ------ ---------------------- --- ---

- --- ---------------

- --- ------ ------ ------------------- --- --- ----

+ - -------- ------------ ------ -------- -------

- --- -------------------------

------ ------ ---------------- --- --- . --- ---

- / --- --- --------------

41

--- --- --- --- ---

- --- --------------------

--- --- --- ---

- ------ ----

--- ---

40

– --- --- --- – --- --- -------------------------------------------------------------------------- --- --- --- – --- + --

- --- --- --- --- --- --------------

--- ---

------ ------------------- --- --- --- ---

--- --- ---

– + - -------- -------- ---------------------------- ------ - --- --- --- --- . ------

--- ---- ----------------- / --- ----

0 ---

--- + --- – --- ---------------------------------------------------------

--- – --- ------ --

--- ---------------

- ------------------- ------ --- --- ----

- --- ---

--------- --- --------- ------ ---

------ ---------------- ------ --- ---

- --- -----

- ------------------- -----

- --- ----

- ------ --- -----

------ ------ ----------------- --- ---

+– - -------- -------- --------------------- ------ -------

------ ------ ---------------------- --- ---

- --- ---------------

- --- ------ ------ ------------------- --- --- ----

+ - -------- ------------ ------ -------- -------

- --- -------------------------

------ ------ ---------------- --- --- . --- ---

- / --- --- --------------

41

+ - ------------ --- --- ,' --- --- ------

--- ,' ---

,-#-9'

+ - -------- --------------- ------ ------ , -#-< ------

,-#-9'

------ ------ --------------- --- ,-#-9<

'

H %,, #%6 2.6 % #6$ % H% 1 -. -#-9'.6 % : # %, *% ':-. %$ %,#' )%(,%2.6 %%-9''.69, %(-!#'#%66 %#' – -- - --- --- --- --- ------------- --- --------------- – --- – + + - ----------- ------ ----------------------- ---------- – – –

---

--- ---

– + --– + --– -- --- ---------------------------- ----------------- ---------- --------- – –– – – -- – –

42

) ---

) ) ),%( #$ %' % F" )7(#' % ------ ),%(#$%' % F"

------ % )#'

+%(%9'$#5,#',,@

+ F"#$#% #' -----------------, + ,

+%(%9'$#',,@ F"#$

+ - #% #' ----------------, – ,

a

– – + - ------------------------------ ------------- ----------------------------------- -----------------------

)

% % % %> >

+ + - ----------- ------ --------------- ----------------------- – – –

- ----

- 9' ----

–

- --- --- ,' --- ----

–

- --------- --- --- -------------

- ---- - -------,' ----

+ -------------

x

b

+

" 2. %

43

+ - ------------ --- --- ,' --- --- ------

--- ,' ---

,-#-9'

+ - -------- --------------- ------ ------ , -#-< ------

,-#-9'

------ ------ --------------- --- ,-#-9<

'

H %,, #%6 2.6 % #6$ % H% 1 -. -#-9'.6 % : # %, *% ':-. %$ %,#' )%(,%2.6 %%-9''.69, %(-!#'#%66 %#' – -- - --- --- --- --- ------------- --- --------------- – --- – + + - ----------- ------ ----------------------- ---------- – – –

---

--- ---

– + --– + --– -- --- ---------------------------- ----------------- ---------- --------- – –– – – -- – –

42

) ---

) ) ),%( #$ %' % F" )7(#' % ------ ),%(#$%' % F"

------ % )#'

+%(%9'$#5,#',,@

+ F"#$#% #' -----------------, + ,

+%(%9'$#',,@ F"#$

+ - #% #' ----------------, – ,

a

– – + - ------------------------------ ------------- ----------------------------------- -----------------------

)

% % % %> >

+ + - ----------- ------ --------------- ----------------------- – – –

- ----

- 9' ----

–

- --- --- ,' --- ----

–

- --------- --- --- -------------

- ---- - -------,' ----

+ -------------

x

b

+

" 2. %

43

(

( ( > -1, > ----------- --- ---

> -1, --- > ---

= -1, = --- ---

--- > --- -1, --- > ---

) -1, - ) =-1, = - ) =-1, = - )

> -1, > - )

-1, - )

= = - (4 ''(4 (4 ''(4 (4 ''(4

- (4 ''(4 ----

(4 ''(4 --- (4 ''(4

44

(4#' '(4#' '(4#' (4#' &!'%(9,(4#' +,' '(4#' 0#' 0#' 0'#' 0#' 0#' 0'#'

>>

> >

>> > > >> >> H'

?#'9.(>>

?#''---, MMMM MMMMMMMMMMMM H' ?9.( ?'---, MM>MM '> N'-%>=>'!#%< ",(" %(4 + ------------- > >

*%9!9(%$:5 5-9,O

[ –3

0

) 4

45

x

(

( ( > -1, > ----------- --- ---

> -1, --- > ---

= -1, = --- ---

--- > --- -1, --- > ---

) -1, - ) =-1, = - ) =-1, = - )

> -1, > - )

-1, - )

= = - (4 ''(4 (4 ''(4 (4 ''(4

- (4 ''(4 ----

(4 ''(4 --- (4 ''(4

44

(4#' '(4#' '(4#' (4#' &!'%(9,(4#' +,' '(4#' 0#' 0#' 0'#' 0#' 0#' 0'#'

>>

> >

>> > > >> >> H'

?#'9.(>>

?#''---, MMMM MMMMMMMMMMMM H' ?9.( ?'---, MM>MM '> N'-%>=>'!#%< ",(" %(4 + ------------- > >

*%9!9(%$:5 5-9,O

[ –3

0

) 4

45

x

Ê ïàðàãðàôó 2 N

?

M MM MMMM MM M M MM MMMM MM M MMMMMMMM

?- >#'%#'#' N= N-%(,MMMM ?-#$ %(#'MM-#$MM #!9'4(- " -# % " # %

( ( ( ) )

),%( -# % #

)!#' 6 ,

'!'95"#' %< #('1-!#''

46

47

),%("

Ê ïàðàãðàôó 2 N

?

M MM MMMM MM M M MM MMMM MM M MMMMMMMM

?- >#'%#'#' N= N-%(,MMMM ?-#$ %(#'MM-#$MM #!9'4(- " -# % " # %

( ( ( ) )

),%( -# % #

)!#' 6 ,

'!'95"#' %< #('1-!#''

46

47

),%("

Ê ïàðàãðàôó 3 &#'%##' 0'(,#''$ &#'%#'#'0''(,#''$ &#'%##' 0'(,#''$ &#'%#'#' 0''(,#''$ 8% 0''(,#''$ 8% 0'(,#''$ 8% 0'(,#''$ 8% 0''(,#''$ 8% 0''(,#''$ 8% 0'(,#''$ 8% 0''(,#''$ 8% 0''(,#''$ 8% 0'(,#''$ 8% 0''(,#''$ ;#''''5

48

;#''' ;#''' ;#''''5 D,( %'9.(2('. M M= MM MM ?- ?- ?- ) : ,#'' '%#''.5 '( ),#'''5' K%' ''"'5,1",#''$'9.( '- ),%( 0'(,#''$ F"' ' )',#'''(#'.5 ),%( 0'(,#''$ F"'' )',#'''(#'.5 ),%( 0'(,#''$ F"'' ---

)' --- ,#'''(#'.5 1

49

Ê ïàðàãðàôó 3 &#'%##' 0'(,#''$ &#'%#'#'0''(,#''$ &#'%##' 0'(,#''$ &#'%#'#' 0''(,#''$ 8% 0''(,#''$ 8% 0'(,#''$ 8% 0'(,#''$ 8% 0''(,#''$ 8% 0''(,#''$ 8% 0'(,#''$ 8% 0''(,#''$ 8% 0''(,#''$ 8% 0'(,#''$ 8% 0''(,#''$ ;#''''5

48

;#''' ;#''' ;#''''5 D,( %'9.(2('. M M= MM MM ?- ?- ?- ) : ,#'' '%#''.5 '( ),#'''5' K%' ''"'5,1",#''$'9.( '- ),%( 0'(,#''$ F"' ' )',#'''(#'.5 ),%( 0'(,#''$ F"'' )',#'''(#'.5 ),%( 0'(,#''$ F"'' ---

)' --- ,#'''(#'.5 1

49

'!.6#' ?''%$-1,'< ',#'''2.6'5

)!#''%(6 %#'',:%6$. '!%'95#'',: H 6 %, $6 # 2' 8% = #$ %(9"!,#''5-9('-#$#< ' #'%#'#!9' G'5' G'5' ) %,''.6#.9'5#'

N-,% '5%$2 '( ''",#''$ F" 092 % )< , %.#%$ ' # 2.6 '9$

50

, ;#%6< #'" ,, P'$ #%"'" %< %#,#'' 'I , # / ),%( #5 5 !"# 5 " -#.5 5!"# 5 H%"'!"#< 5 -,%#:%%#$ 5 5 -#.5 5 % 5 #5 0 5

K.

+

3, %

33, %

P'$ '3, %,%#,# !(4%< %#,#'' ' -# , % ,% %'. ' #< 0,%

K.

+

D4

Q'5

R

;Q'$%'#!(4 +%#,#'' ,D4 ,Q'$ 0

51

'!.6#' ?''%$-1,'< ',#'''2.6'5

)!#''%(6 %#'',:%6$. '!%'95#'',: H 6 %, $6 # 2' 8% = #$ %(9"!,#''5-9('-#$#< ' #'%#'#!9' G'5' G'5' ) %,''.6#.9'5#'

N-,% '5%$2 '( ''",#''$ F" 092 % )< , %.#%$ ' # 2.6 '9$

50

, ;#%6< #'" ,, P'$ #%"'" %< %#,#'' 'I , # / ),%( #5 5 !"# 5 " -#.5 5!"# 5 H%"'!"#< 5 -,%#:%%#$ 5 5 -#.5 5 % 5 #5 0 5

K.

+

3, %

33, %

P'$ '3, %,%#,# !(4%< %#,#'' ' -# , % ,% %'. ' #< 0,%

K.

+

D4

Q'5

R

;Q'$%'#!(4 +%#,#'' ,D4 ,Q'$ 0

51

),%(, '9'.- ('",! '5 F" %%'2#'" F' #'( ' %'2'(4 - %'2!< ' '5 (4 '5 9 %%'2#' F" , '9'.- ('",! '5 ),%(%#.-''$!! '5"#%(!!%%< ! !5 F#'(#.-'$'!5 (4 !5!!#.-''(4 ' '$ ! '5 % #%6 !5 9' #.!(' F" S#.-''$!! '5 ),%( !,' % " -% #.-''$ ,!'< '.65%#5-, #'!,''< , %,-1, !,' %

Ã ë à â à II ÔÓÍÊÖÈÈ

§ 4. Ôóíêöèè è èõ ãðàôèêè 10. ×òî òàêîå ôóíêöèÿ +& & + + & + + ?- +,& P' '$& %(-'$ I,'2 T%( -< '$ 0 %#5-9, &' + & ' ' + T' T' (2 (( '-' %'2 % H''%, (2 2( T%(-'$0'9%#',('.6 % T%(!' '5 0 %

52

53

),%(, '9'.- ('",! '5 F" %%'2#'" F' #'( ' %'2'(4 - %'2!< ' '5 (4 '5 9 %%'2#' F" , '9'.- ('",! '5 ),%(%#.-''$!! '5"#%(!!%%< ! !5 F#'(#.-'$'!5 (4 !5!!#.-''(4 ' '$ ! '5 % #%6 !5 9' #.!(' F" S#.-''$!! '5 ),%( !,' % " -% #.-''$ ,!'< '.65%#5-, #'!,''< , %,-1, !,' %

Ã ë à â à II ÔÓÍÊÖÈÈ

§ 4. Ôóíêöèè è èõ ãðàôèêè 10. ×òî òàêîå ôóíêöèÿ +& & + + & + + ?- +,& P' '$& %(-'$ I,'2 T%( -< '$ 0 %#5-9, &' + & ' ' + T' T' (2 (( '-' %'2 % H''%, (2 2( T%(-'$0'9%#',('.6 % T%(!' '5 0 %

52

53

",'!' '$",'%,9 % !' '$I,'20 % ) - 1- . #.-,7' # 1< -0#

),%( #. %' -#', ! H 3 !#, #(%$ #.#'%' #< . L!33 !#,#.(%$ #.#'%< '%$ F#.%'-#',%%#,#'' #.%'-#', !

B

0

1

T%(-'$%%!#%6 % - T%( -'$ %% ! #%6 % ---------- –

----------- T%( -'$ %% ! #%6 % +

D

– ---------------- T%(-'$%%!#%6 %

x

A

11. Âû÷èñëåíèå çíà÷åíèé ôóíêöèè ïî ôîðìóëå

------

------ –

------ –

------

------

--

------ –

C 1

# $

y

--- --- --- ---

---

---

-

--- --------------------

- - --- ------------

------

54

--- ---------

55

",'!' '$",'%,9 % !' '$I,'20 % ) - 1- . #.-,7' # 1< -0#

),%( #. %' -#', ! H 3 !#, #(%$ #.#'%' #< . L!33 !#,#.(%$ #.#'%< '%$ F#.%'-#',%%#,#'' #.%'-#', !

B

0

1

T%(-'$%%!#%6 % - T%( -'$ %% ! #%6 % ---------- –

----------- T%( -'$ %% ! #%6 % +

D

– ---------------- T%(-'$%%!#%6 %

x

A

11. Âû÷èñëåíèå çíà÷åíèé ôóíêöèè ïî ôîðìóëå

------

------ –

------ –

------

------

--

------ –

C 1

# $

y

--- --- --- ---

---

---

-

--- --------------------

- - --- ------------

------

54

--- ---------

55

3

%

"

0

+, , @ + + , , @

T%(-'$15I,'20',('. % #: (' / ),%( 4%%%' % '" " %%< %' % '" H%" % '" - ,%#: #' +%# ,#'' '" %%%'% '"

B

1

----------- %

+& + +& & & & &

5

y

M 1

x

A

12. Ãðàôèê ôóíêöèè

!"#

y 10

0

1

x

4

y

N

1 0

1

K

x

y 8

1

M

–1 0

56

57

1

5

x

3

%

"

0

+, , @ + + , , @

T%(-'$15I,'20',('. % #: (' / ),%( 4%%%' % '" " %%< %' % '" H%" % '" - ,%#: #' +%# ,#'' '" %%%'% '"

B

1

----------- %

+& + +& & & & &

5

y

M 1

x

A

12. Ãðàôèê ôóíêöèè

!"#

y 10

0

1

x

4

y

N

1 0

1

K

x

y 8

1

M

–1 0

56

57

1

5

x

---

---

---

---

---

---

y

6

0 1

6

x

y N

1 0

1

x P

% &#'%##' F %-'9"I,I,'2 " &#'%##' F "-'9"I,I,'2 # &#'%#'#' F #'-'9"I, I,'2 ?- $ -'9"I,I,'2 )'-'9"I,I,'2 % &#'%##' F %-'9"I, " &#'%##' F "-'9"I, # &#'%#'#' F #'-'9"I,

1

58

x B

M

y

0

3 3

1 1

A

C

1

y

0

)9('.!' '$I,'2'-- T2('.!' '$I,'2'--

1

x

59

---

---

---

---

---

---

y

6

0 1

6

x

y N

1 0

1

x P

% &#'%##' F %-'9"I,I,'2 " &#'%##' F "-'9"I,I,'2 # &#'%#'#' F #'-'9"I, I,'2 ?- $ -'9"I,I,'2 )'-'9"I,I,'2 % &#'%##' F %-'9"I, " &#'%##' F "-'9"I, # &#'%#'#' F #'-'9"I,

1

58

x B

M

y

0

3 3

1 1

A

C

1

y

0

)9('.!' '$I,'2'-- T2('.!' '$I,'2'--

1

x

59

)"I,

y

1

10

)I,

- -----

------

4,7

1 0 1 2,5 " " "

x

m, êã 5

--- --- --- --- =

4

------ --- $ --- % &'(! --- --- --- --- % '

2 1

*!' 0 °C + 100 *! ' 0 + *! ' 0+ 80 *!' 0 60 + + 0 ! 40 ',. + 0 ! 20 ',.

+ 0 ! 0 ',.

–+ - -------- -------- -------- --------------------- --- --- --- --- -----

3

0

),%("#.64'. ",!#.6 4, )%< -, '$ "#.6 4' 6 % 4' ",!#.6% 4' P'$ "#.6< 4'%'(4%%#,#'' U"#.64'. ",!#.6 0 ##-.#%"#4'

1

2

3

4

5

6 V, ë

> $ $ $ = ?#'%# > '#'

§ 5. Ëèíåéíàÿ ôóíêöèÿ 13. Ëèíåéíàÿ ôóíêöèÿ è åå ãðàôèê V!#%%($#$%$'5'5I,'25

2

4

6

8

10 12 ìèí

?%,6%I(0 ?%I(0 )"0 ?%,6%I( 0' @ H9( 0 @ )" 0 @

60

6 6 6 U'5'5$#$%$!#%%(6 V!#%%($#$%$'5'5I,'25 N --- ? ?

61

)"I,

y

1

10

)I,

- -----

------

4,7

1 0 1 2,5 " " "

x

m, êã 5

--- --- --- --- =

4

------ --- $ --- % &'(! --- --- --- --- % '

2 1

*!' 0 °C + 100 *! ' 0 + *! ' 0+ 80 *!' 0 60 + + 0 ! 40 ',. + 0 ! 20 ',.

+ 0 ! 0 ',.

–+ - -------- -------- -------- --------------------- --- --- --- --- -----

3

0

),%("#.64'. ",!#.6 4, )%< -, '$ "#.6 4' 6 % 4' ",!#.6% 4' P'$ "#.6< 4'%'(4%%#,#'' U"#.64'. ",!#.6 0 ##-.#%"#4'

1

2

3

4

5

6 V, ë

> $ $ $ = ?#'%# > '#'

§ 5. Ëèíåéíàÿ ôóíêöèÿ 13. Ëèíåéíàÿ ôóíêöèÿ è åå ãðàôèê V!#%%($#$%$'5'5I,'25

2

4

6

8

10 12 ìèí

?%,6%I(0 ?%I(0 )"0 ?%,6%I( 0' @ H9( 0 @ )" 0 @

60

6 6 6 U'5'5$#$%$!#%%(6 V!#%%($#$%$'5'5I,'25 N --- ? ?

61

---

y

1 1 0

1

0 1

x

y

0 1

x

y

1

1

1 0 1

x

0 1

62

x

0 1

x

y 1 1 x

1 0 1

y

0 1

x

y

y

0 1

x

1

1

y

y

y

> 1

x

63

0 1

x

---

y

1 1 0

1

0 1

x

y

0 1

x

y

1

1

1 0 1

x

0 1

62

x

0 1

x

y 1 1 x

1 0 1

y

0 1

x

y

y

0 1

x

1

1

y

y

y

> 1

x

63

0 1

x

y

1 0 1

x

y,°C 100

80 *! ' + *! 60 ' + N +#'< 40 "%( ! ' 20 0

1 0 1

70

20 30

40 50

60 x, ìèí

y

10

x

y

60

WI-%%( #

50

3 3 3

---

40

---

30

WI-%%( #

20 10 0 1 –10 –20

64

3

5

x

---

% WI-6 !'',: , " WI-6 !'',: , # WI'-6 !'',: , $ WI-6 !'',: ,

65

y

1 0 1

x

y,°C 100

80 *! ' + *! 60 ' + N +#'< 40 "%( ! ' 20 0

1 0 1

70

20 30

40 50

60 x, ìèí

y

10

x

y

60

WI-%%( #

50

3 3 3

---

40

---

30

WI-%%( #

20 10 0 1 –10 –20

64

3

5

x

---

% WI-6 !'',: , " WI-6 !'',: , # WI'-6 !'',: , $ WI-6 !'',: ,

65

#2

y = –1 y = –5

N$#$%$ ---

N ?

y = 3,2 y=0

N$#$%$

1 0 1

x

y = 1,6 y = –1,9

1 0 1

x

y = –2

> > N(,-#('5- N(,'-#('5-

--- --- --- --- ---

---

--- --- ---

--- --- --- ---

--- ---

---

---

--- ---

--- --- ---

---

---

---

y

1

0

x

–x

67

1 =

y

x

,5 –1

---

66

?

y=

/ ),%(-#$"!"# 5"#$ !"# 5($0 H%"!"# 5 -,%#:#' $ +%#,#'' -#$"!"#5#$0 5($0 5

x

y

+&

y= 3x

y=7

y=6

14. Ïðÿìàÿ ïðîïîðöèîíàëüíîñòü

=

y

WI ''.6 I,'< 25 0 -$. -< ('.%

y

WI ''.6 I,'< 25 0 -$. -< ('.%

#2

y = –1 y = –5

N$#$%$ ---

N ?

y = 3,2 y=0

N$#$%$

1 0 1

x

y = 1,6 y = –1,9

1 0 1

x

y = –2

> > N(,-#('5- N(,'-#('5-

--- --- --- --- ---

---

--- --- ---

--- --- --- ---

--- ---

---

---

--- ---

--- --- ---

---

---

---

y

1

0

x

–x

67

1 =

y

x

,5 –1

---

66

?

y=

/ ),%(-#$"!"# 5"#$ !"# 5($0 H%"!"# 5 -,%#:#' $ +%#,#'' -#$"!"#5#$0 5($0 5

x

y

+&

y= 3x

y=7

y=6

14. Ïðÿìàÿ ïðîïîðöèîíàëüíîñòü

=

y

WI ''.6 I,'< 25 0 -$. -< ('.%

y

WI ''.6 I,'< 25 0 -$. -< ('.%

1

0 y= 2,5x

x

y= –0 ,5

x

1 0

y

10

5

0 1

1

x

% ---

1 0

-

1

x

%

)'9 "

?-'9 "

--- ---

---

?-'9

68

x

)46.#-, #%-% )46-#%-% +%(-46 @ #%-% @ H%-%-6! #!(< 4 -4-46 % XY-'9"I, " )'9"I, # )'9"I, $ )'9"I,

y

5

)*

P#%%( -< 9''!I,

-

-

- P' ' - %,7%#,

y

1

4,5x y=–

y

)'9

69

1

0 y= 2,5x

x

y= –0 ,5

x

1 0

y

10

5

0 1

1

x

% ---

1 0

-

1

x

%

)'9 "

?-'9 "

--- ---

---

?-'9

68

x

)46.#-, #%-% )46-#%-% +%(-46 @ #%-% @ H%-%-6! #!(< 4 -4-46 % XY-'9"I, " )'9"I, # )'9"I, $ )'9"I,

y

5

)*

P#%%( -< 9''!I,

-

-

- P' ' - %,7%#,

y

1

4,5x y=–

y

)'9

69

#

#

---

---

?-'9

$ --- ---

$ --- ---

--- ---

0

--- --- --- --- ---

--- --- --- $ --- ---

?-'9 )

?-'9 )

---

y

1 x

0 1

x

>

0

1

1 1

x

0 1

x

>

=

--- =

--- >

15. Âçàèìíîå ðàñïîëîæåíèå ãðàôèêîâ ëèíåéíûõ ôóíêöèé WI-('. WI-%:%$ WI-%:%$

70

x

=

y

y

1

0

x

33 = --- 333 > --- --- --- 3Z > ---

y

1 0 1

1

3 = ---

1

)'9

)'9

>

y

1

--- ---

y

?-'9

=

WI-%:%$ WI-('. WI-%:%$

71

#

#

---

---

?-'9

$ --- ---

$ --- ---

--- ---

0

--- --- --- --- ---

--- --- --- $ --- ---

?-'9 )

?-'9 )

---

y

1 x

0 1

x

>

0

1

1 1

x

0 1

x

>

=

--- =

--- >

15. Âçàèìíîå ðàñïîëîæåíèå ãðàôèêîâ ëèíåéíûõ ôóíêöèé WI-('. WI-%:%$ WI-%:%$

70

x

=

y

y

1

0

x

33 = --- 333 > --- --- --- 3Z > ---

y

1 0 1

1

3 = ---

1

)'9

)'9

>

y

1

--- ---

y

?-'9

=

WI-%:%$ WI-('. WI-%:%$

71

)%:%$

–x +

y = –x – 1,5 y y = 0,5x + 2,5 y = 2,5

6

=

x

3

1

–

72

0

–x

)%:%$

)%:%$

y

1 =

1 0 1

x

y = x + 2,5 y = –x + 2,5

y

y = 3x

1

73

0

1

y= 3x – 4

3

0'. -% '$ 0'. -% '$

0'. -% '$

0'. -% '$

0'. -% '$ 0'. -% '$

–x

y

y =

---

?-%:%$

y

---

y= 3x + 1,2

WI-('.,I,'25

WI-%:%$,I,'25

x

)%:%$

–x +

y = –x – 1,5 y y = 0,5x + 2,5 y = 2,5

6

=

x

3

1

–

72

0

–x

)%:%$

)%:%$

y

1 =

1 0 1

x

y = x + 2,5 y = –x + 2,5

y

y = 3x

1

73

0

1

y= 3x – 4

3

0'. -% '$ 0'. -% '$

0'. -% '$

0'. -% '$

0'. -% '$ 0'. -% '$

–x

y

y =

---

?-%:%$

y

---

y= 3x + 1,2

WI-('.,I,'25

WI-%:%$,I,'25

x

2

0 1

x

>

------ > =

> =

–x –

2

y

y= 17x + 20

40

y 0x y = –3

50

30 20 10 0 1

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå II Ê ïàðàãðàôó 4 - ---------

50

">M M T%(-'$0#% M M =

40

------ @ , +--

30

&

10 x

–20

–20

–30

–30

–40

–40

74

0x + 8 y = –3

0 1 –10

'0-#.5-#'0#5 0!-#.5 % 0!-%'5 0'-#. 0'#.

20

–10 y= 17x

33 >

=

WI%-9'#3333''.6 < #$6

WI%-9'#333Z''.6 < #$6

=

y

–2 ,4x 0 y=

1

),%(#3'(!#! !'# 33 0 !' H%"!#! !' -,%#:#' #3'(!#! !'

–

3 =

x

y

=

y

x

'!#%$-''$ !#%$

-

-

-

75

2

0 1

x

>

------ > =

> =

–x –

2

y

y= 17x + 20

40

y 0x y = –3

50

30 20 10 0 1

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå II Ê ïàðàãðàôó 4 - ---------

50

">M M T%(-'$0#% M M =

40

------ @ , +--

30

&

10 x

–20

–20

–30

–30

–40

–40

74

0x + 8 y = –3

0 1 –10

'0-#.5-#'0#5 0!-#.5 % 0!-%'5 0'-#. 0'#.

20

–10 y= 17x

33 >

=

WI%-9'#3333''.6 < #$6

WI%-9'#333Z''.6 < #$6

=

y

–2 ,4x 0 y=

1

),%(#3'(!#! !'# 33 0 !' H%"!#! !' -,%#:#' #3'(!#! !'

–

3 =

x

y

=

y

x

'!#%$-''$ !#%$

-

-

-

75

+ - ------- –---------------------

+ - ------- –--------------------

+ - ------- ---------------

y

H% % H% % -----------------

1 0

1

–2 0 2

76

12

x

x

1

---

1 –2

5

0

x

y

y

1

–2

x

–14

+ -----------

---

–2 1 0 2

–10

y

) ) > > ) > =

77

+ - ------- –---------------------

+ - ------- –--------------------

+ - ------- ---------------

y

H% % H% % -----------------

1 0

1

–2 0 2

76

12

x

x

1

---

1 –2

5

0

x

y

y

1

–2

x

–14

+ -----------

---

–2 1 0 2

–10

y

) ) > > ) > =

77

8% % 8% %

),%( ) !' 'I,'2#'!' ':",' ),%(

V, ë 25 20 15 10 5 0

------ ---

2

4

6

8

H, ñì

) --- !' 'I,'2-#-9'!' ':

10 12 14 16

",' T! T!.#4 '09 ..#'! *! -% #.6 ! .# . ' %< %$' ?%%$''. ! -% #.6'-,, ! -%#.6'-,< '

------ @ +'$$%%(''-,<

$9

– ----------------

E#$%$

E#$%$ ?$#$%$ E#$%$ E#$%$

E#$%$

) !' )%(, - L

Ê ïàðàãðàôó 5

) !' )%(, - L

+'$$%%('-,, --- ---

78

) -

- )1, )##- 1,I,,,9%$ '#'

V'5'$I,'2$

79

8% % 8% %

),%( ) !' 'I,'2#'!' ':",' ),%(

V, ë 25 20 15 10 5 0

------ ---

2

4

6

8

H, ñì

) --- !' 'I,'2-#-9'!' ':

10 12 14 16

",' T! T!.#4 '09 ..#'! *! -% #.6 ! .# . ' %< %$' ?%%$''. ! -% #.6'-,, ! -%#.6'-,< '

------ @ +'$$%%(''-,<

$9

– ----------------

E#$%$

E#$%$ ?$#$%$ E#$%$ E#$%$

E#$%$

) !' )%(, - L

Ê ïàðàãðàôó 5

) !' )%(, - L

+'$$%%('-,, --- ---

78

) -

- )1, )##- 1,I,,,9%$ '#'

V'5'$I,'2$

79

y

1

x 0 1

G'. -% '$ "I % %$ < '

- -

y

500 400 300 200 100

5 4 3 2 1

0

2 3 4

x

F %-'9"I,% ---

---

1

9-'(2. !' '$

200 400 0 100 300 x

% WI-6 ! ,% 4 WI-6 ! ,4

–1 0 1

x

êì 75

60

P #%-%-< ! ' ?-,(# #%< -%! ' & [ & [

80

y

y

1

6 WI'-6 ! ,6 7 WI'-6 ! ,7

45 30 15 0

1

2

3

4

5

, @% , @%

)% 0'. -% '$ )% 0'. -% '$ )% 0'. -% '$

81

÷

y

1

x 0 1

G'. -% '$ "I % %$ < '

- -

y

500 400 300 200 100

5 4 3 2 1

0

2 3 4

x

F %-'9"I,% ---

---

1

9-'(2. !' '$

200 400 0 100 300 x

% WI-6 ! ,% 4 WI-6 ! ,4

–1 0 1

x

êì 75

60

P #%-%-< ! ' ?-,(# #%< -%! ' & [ & [

80

y

y

1

6 WI'-6 ! ,6 7 WI'-6 ! ,7

45 30 15 0

1

2

3

4

5

, @% , @%

)% 0'. -% '$ )% 0'. -% '$ )% 0'. -% '$

81

÷

0'. -% '$ 0'. -% '$

)% 0'. -% '$ ?-% ?-%

y

y y =

y= ax x

1 1 0

x

= y

5

F 5-'9"I, F -$$ -(' "I, I,'2 I,'2$!%$I,5

)%(,-$$-6 < !% T' ('

y

1 0 1

? '9#',,"('

A(2; 3) 0

1

x

0'. -% '$

0'. -% '$

82

x

y = –2x + 3

y

1

y = 3x + 2

y = 0,5x – 2

ax

0 1

bx

1

bx y=

83

0'. -% '$ 0'. -% '$

)% 0'. -% '$ ?-% ?-%

y

y y =

y= ax x

1 1 0

x

= y

5

F 5-'9"I, F -$$ -(' "I, I,'2 I,'2$!%$I,5

)%(,-$$-6 < !% T' ('

y

1 0 1

? '9#',,"('

A(2; 3) 0

1

x

0'. -% '$

0'. -% '$

82

x

y = –2x + 3

y

1

y = 3x + 2

y = 0,5x – 2

ax

0 1

bx

1

bx y=

83

Ã ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

§ 6. Ñòåïåíü è åå ñâîéñòâà 16. Îïðåäåëåíèå ñòåïåíè ñ íàòóðàëüíûì ïîêàçàòåëåì --- --- --- --- ---

!

!

--- --- %'#' 0-!(

--- --- --- --- --- ---

-

--- --- --- --- --- -------

0%'#' 0-!( 0%'#' 0-!( 0%'#' 0-!( 0%'#' 0-!(

84

- --- --- --- --- --- --- -------

--- --- --- ---

0%'#' 0-!(

--------- ------ --- --- --- --- --- ---

--------- ---

--- --- --- --- ---

-

--- --- --- --- --- --- ----

- --- --- --- --- --- --- --- ----

85

Ã ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

§ 6. Ñòåïåíü è åå ñâîéñòâà 16. Îïðåäåëåíèå ñòåïåíè ñ íàòóðàëüíûì ïîêàçàòåëåì --- --- --- --- ---

!

!

--- --- %'#' 0-!(

--- --- --- --- --- ---

-

--- --- --- --- --- -------

0%'#' 0-!( 0%'#' 0-!( 0%'#' 0-!( 0%'#' 0-!(

84

- --- --- --- --- --- --- -------

--- --- --- ---

0%'#' 0-!(

--------- ------ --- --- --- --- --- ---

--------- ---

--- --- --- --- ---

-

--- --- --- --- --- --- ----

- --- --- --- --- --- --- --- ----

85

- ------ -------

------ ------ --- ---

- --- ------ --------- --- --- ----

------ --- --- ---

------ ------ --- ---

= > -1, > > = -1, > = > -1,=

86

------ ------ --- ---

- ------ --------- --- --- -----------

---

) ) ) ) )

) )

87

- ------ -------

------ ------ --- ---

- --- ------ --------- --- --- ----

------ --- --- ---

------ ------ --- ---

= > -1, > > = -1, > = > -1,=

86

------ ------ --- ---

- ------ --------- --- --- -----------

---

) ) ) ) )

) )

87

) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

) )

- : '$ %-'( :" % %( % '2(' = %#(' -: -: '$%-'(:" %%( %'2(' =-:1%,'2(< '" %-9('" Q'" ' =-:

88

G#%,. % +,## % G#!'% % &!'%(## % G,!'% % +,,# %

;#''.5#!'% % ;''$%,## %

) ) )

0'. -% '$ 0'. -% '$ WI-('. WI-%:%$

17. Óìíîæåíèå è äåëåíèå ñòåïåíåé

'''

89

) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

) )

- : '$ %-'( :" % %( % '2(' = %#(' -: -: '$%-'(:" %%( %'2(' =-:1%,'2(< '" %-9('" Q'" ' =-:

88

G#%,. % +,## % G#!'% % &!'%(## % G,!'% % +,,# %

;#''.5#!'% % ;''$%,## %

) ) )

0'. -% '$ 0'. -% '$ WI-('. WI-%:%$

17. Óìíîæåíèå è äåëåíèå ñòåïåíåé

'''

89

'''''

'''

– ----------------- –

--- --------------- --- --- --- --- --- – --- ---------

------ ------------------ --- --- – --

- -------- --------------

- -------- --------------

- ------------- ------------------------

------ --- --- --- --- ---

90

'''

---------

------

- -------- -----------------

- --- --- --- ----

-

---

- ---

- - --- ---

- --- --- ----

91

'''''

'''

– ----------------- –

--- --------------- --- --- --- --- --- – --- ---------

------ ------------------ --- --- – --

- -------- --------------

- -------- --------------

- ------------- ------------------------

------ --- --- --- --- ---

90

'''

---------

------

- -------- -----------------

- --- --- --- ----

-

---

- ---

- - --- ---

- --- --- ----

91

18. Âîçâåäåíèå â ñòåïåíü ïðîèçâåäåíèÿ è ñòåïåíè

------ --- --- ---

------ --- --- ---

y

1

0 1

8% 8% +,&+& & ' &

+ + +

-: = > % F %-'9"I, " F "-'9"I, % G,%"'\%#% " G,%"'\ %#% " ------ ---------

----------------------------- "

92

x

! !

),%( %'# F"-7(# 8%%'##' )7(,# %$# ! 0%'# )7(,# < %$# ! +'#0 )7(,#< %$# ! +'#0 )7(,#< %$#!

),%(, F""\ T\,# %$# !

93

18. Âîçâåäåíèå â ñòåïåíü ïðîèçâåäåíèÿ è ñòåïåíè

------ --- --- ---

------ --- --- ---

y

1

0 1

8% 8% +,&+& & ' &

+ + +

-: = > % F %-'9"I, " F "-'9"I, % G,%"'\%#% " G,%"'\ %#% " ------ ---------

----------------------------- "

92

x

! !

),%( %'# F"-7(# 8%%'##' )7(,# %$# ! 0%'# )7(,# < %$# ! +'#0 )7(,#< %$# ! +'#0 )7(,#< %$#!

),%(, F""\ T\,# %$# !

93

T\,# %$#!

T\,# %$#!

T\,# %$#!

! !

--- --- --- ---

---

--- --- --- --- --- --- ---

- ------------------- -------- -----------------------

94

- ------------------- -------- ----------------------

- ---------------- -------- -----------

- -------- ------ --- --------------- --------------

> > = = = %

) ) ) -

-

95

T\,# %$#!

T\,# %$#!

T\,# %$#!

! !

--- --- --- ---

---

--- --- --- --- --- --- ---

- ------------------- -------- -----------------------

94

- ------------------- -------- ----------------------

- ---------------- -------- -----------

- -------- ------ --- --------------- --------------

> > = = = %

) ) ) -

-

95

§ 7. Îäíî÷ëåíû 19. Îäíî÷ëåí è åãî ñòàíäàðòíûé âèä

N

?

N ?Y

N N

?

N

N N

N N

%

N

?

?

N

N

?

J' % N' % H.% % %

G1II2' G1II2' G1II2' G1II2' --- --- G1II2'

--- --- --- ---

+-'( +-'(

+-'( [-'(

+-'( +-'(

T'.0-#-9'. % " Q%2%%.0-#-9'. % " G'.0-#-9'. % " ---

G1II2'

'('('(

---

---

--- --- --- ---

---

--- --- --- --- ---

- --- --- -----------------------

- --- ---------------------

--- ---

---

--- ---

---

- --- –------------

---

- --- --- ------ --- --- --- ------ --- --- ------ ----

– - ---------------------------

96

–

---

–

97

§ 7. Îäíî÷ëåíû 19. Îäíî÷ëåí è åãî ñòàíäàðòíûé âèä

N

?

N ?Y

N N

?

N

N N

N N

%

N

?

?

N

N

?

J' % N' % H.% % %

G1II2' G1II2' G1II2' G1II2' --- --- G1II2'

--- --- --- ---

+-'( +-'(

+-'( [-'(

+-'( +-'(

T'.0-#-9'. % " Q%2%%.0-#-9'. % " G'.0-#-9'. % " ---

G1II2'

'('('(

---

---

--- --- --- ---

---

--- --- --- --- ---

- --- --- -----------------------

- --- ---------------------

--- ---

---

--- ---

---

- --- –------------

---

- --- --- ------ --- --- --- ------ --- --- ------ ----

– - ---------------------------

96

–

---

–

97

----------------- ---------------------- ------ ---- ----

- --------------------------- ----------------------------------- -------- --- -----------------

20. Óìíîæåíèå îäíî÷ëåíîâ. Âîçâåäåíèå îäíî÷ëåíà â ñòåïåíü

- --- --- --- --------------

--- ---

--- ---

--- --- --- ---

98

S

--- ---

- --- ----

99

----------------- ---------------------- ------ ---- ----

- --------------------------- ----------------------------------- -------- --- -----------------

20. Óìíîæåíèå îäíî÷ëåíîâ. Âîçâåäåíèå îäíî÷ëåíà â ñòåïåíü

- --- --- --- --------------

--- ---

--- ---

--- --- --- ---

98

S

--- ---

- --- ----

99

--- --- ---

---

---

--- ---

- --- ----

--- '( ' ( --- '(' (

--- '( ('(

100

! #! #!" #!

'('('('('( '( - ------ ------ ----

),%( '5-,%,"( K.

+

T-,%

3%

33%

--- ---

--- --- ---

------ ------------ ---

' ' ' ' '

- ' --- ' ------ ' --- ' ------ ------ '' ' ----

P'$ '33%,"$,#-!(4 %%#,#'' ! '5 ),%( ! '5#3,#!I$'(4 #33 K.

+

)#!

36'7

336'7

P'$ #36'7I$,#!'(< 4 #33%%#,#'' !'5 % "

101

--- --- ---

---

---

--- ---

- --- ----

--- '( ' ( --- '(' (

--- '( ('(

100

! #! #!" #!

'('('('('( '( - ------ ------ ----

),%( '5-,%,"( K.

+

T-,%

3%

33%

--- ---

--- --- ---

------ ------------ ---

' ' ' ' '

- ' --- ' ------ ' --- ' ------ ------ '' ' ----

P'$ '33%,"$,#-!(4 %%#,#'' ! '5 ),%( ! '5#3,#!I$'(4 #33 K.

+

)#!

36'7

336'7

P'$ #36'7I$,#!'(< 4 #33%%#,#'' !'5 % "

101

0'. -% '$ T'. 0-#-9'. % Q%2%%. 0-#-9'. % G'. 0-#-9'. %

21. Ôóíêöèè O = N2 è O = N3 è èõ ãðàôèêè

-

-

-

- >'- -

='- -

-

- ='- -

>'- -

102

),%(%'#%"-7(% 8% %' # % -7( % )7(,# %$# !

- %-7( --------- % 8%%'# ----

)7(,'(4%$#!

*.-7(,# %(#!%',',#< (#! *.-7(,# %(#!%',',#< (#! -

-

- - > >'-- 8%,,# (#!\,# %$# ! 8% , ,'(4( # ! \ ,'(4%$ # ! &,',# (#!

y

1 0

-

103

1

x

0'. -% '$ T'. 0-#-9'. % Q%2%%. 0-#-9'. % G'. 0-#-9'. %

21. Ôóíêöèè O = N2 è O = N3 è èõ ãðàôèêè

-

-

-

- >'- -

='- -

-

- ='- -

>'- -

102

),%(%'#%"-7(% 8% %' # % -7( % )7(,# %$# !

- %-7( --------- % 8%%'# ----

)7(,'(4%$#!

*.-7(,# %(#!%',',#< (#! *.-7(,# %(#!%',',#< (#! -

-

- - > >'-- 8%,,# (#!\,# %$# ! 8% , ,'(4( # ! \ ,'(4%$ # ! &,',# (#!

y

1 0

-

103

1

x

% F %-'9"I,

0'. -% '$

" --- ---

F "-'9"I,

M MM M M MM M M MMM M MMM

- # --- ----

------ --- --- --- --- --- --- ---

- --- ----

--- ------

- ------ ----

F #'-'9"I,

y

§ 8. Àáñîëþòíàÿ è îòíîñèòåëüíàÿ ïîãðåøíîñòè

=

22. Àáñîëþòíàÿ ïîãðåøíîñòü

1 0

>

1

x

>

)7(-,# %$# !-1,%-5< "

M M M M M M M M MM MM

T\ ,# %$ # ! -1, #' -,%$ '

MM MM M M

> = > > = >

M M MM M M M M

104

105

% F %-'9"I,

0'. -% '$

" --- ---

F "-'9"I,

M MM M M MM M M MMM M MMM

- # --- ----

------ --- --- --- --- --- --- ---

- --- ----

--- ------

- ------ ----

F #'-'9"I,

y

§ 8. Àáñîëþòíàÿ è îòíîñèòåëüíàÿ ïîãðåøíîñòè

=

22. Àáñîëþòíàÿ ïîãðåøíîñòü

1 0

>

1

x

>

)7(-,# %$# !-1,%-5< "

M M M M M M M M MM MM

T\ ,# %$ # ! -1, #' -,%$ '

MM MM M M

> = > > = >

M M MM M M M M

104

105

---

–

--- --- ------ --------------- ------ ------ –

--- --- --------- --------------------- --------- --------- –

--- --- ------------ ---------------------------- ------------ ------------

– -------- --------- --- ---------------------------

%"# 584 % '%(:2.6 %5" % '%(:2.6

A

M

B

04'"'2,0%$.6 0'5502.6 00%.6 + - ------ M M> ----------

)9'#.'% '%(: " --- ---

---

– -------- > --------- --------------------------- - – - -------- --------- --- ------------------------------

--------- --------- --------- 0 -9'' !' ' % --

% '%(:

),%( ,%. 4 -4 " ' #,% 6 )4 ' -,( '#,%-6 P'$ #%(-,( %%#,#'' ,%.4-4

106

- ---------------------- ---------------------- ------------------------ --------------

----------- --------- ------ ------ ------ --- ----------------- -----------------

-------------- --------------

34'.#-, ' 334'.#-, ' 34'' #9''(4 @ 0%%(34'. @ 0%%(334'. 334'-.#"'(4 F -% '$ "I# !' 4'. #%%( ! -%' #9'$34'.' %%$'%

23. Îòíîñèòåëüíàÿ ïîãðåøíîñòü ------- ------- /

M M ------- / ----------- / M M M M ------- /

---

M M

M M

-------------- /

- -----

M M

----------------- /

– ------------------------------- -------------- /

----------- /

----------- /

MM

M M

107

---

–

--- --- ------ --------------- ------ ------ –

--- --- --------- --------------------- --------- --------- –

--- --- ------------ ---------------------------- ------------ ------------

– -------- --------- --- ---------------------------

%"# 584 % '%(:2.6 %5" % '%(:2.6

A

M

B

04'"'2,0%$.6 0'5502.6 00%.6 + - ------ M M> ----------

)9'#.'% '%(: " --- ---

---

– -------- > --------- --------------------------- - – - -------- --------- --- ------------------------------

--------- --------- --------- 0 -9'' !' ' % --

% '%(:

),%( ,%. 4 -4 " ' #,% 6 )4 ' -,( '#,%-6 P'$ #%(-,( %%#,#'' ,%.4-4

106

- ---------------------- ---------------------- ------------------------ --------------

----------- --------- ------ ------ ------ --- ----------------- -----------------

-------------- --------------

34'.#-, ' 334'.#-, ' 34'' #9''(4 @ 0%%(34'. @ 0%%(334'. 334'-.#"'(4 F -% '$ "I# !' 4'. #%%( ! -%' #9'$34'.' %%$'%

23. Îòíîñèòåëüíàÿ ïîãðåøíîñòü ------- ------- /

M M ------- / ----------- / M M M M ------- /

---

M M

M M

-------------- /

- -----

M M

----------------- /

– ------------------------------- -------------- /

----------- /

----------- /

MM

M M

107

------- /

– ------- / -----------------------

- / ------------

----------- / ------------------- /

H!' ' " " " "

------------ /

------------ /

H!' '

Q%2%% %'(4%2%%. "#!

------------------- -----------------------------

------------------- ----------------------------- --------------

0'. -% '$% %(:2%% 0'. -% '$% %(:'

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå III Ê ïàðàãðàôó 6 &#'%#'#' &#'%##' )%(,-#!#' %##< -, %' #:7%$' T%:%, 9' #%$2I5

108

F

' #%$2I5 )%9' %

-, %' #:< 7%$'-%(, T%%(!( ' #%$' )1, %

' #%$',!'< %$'

= = > = > >= > =' = ' ='

= '

109

------- /

– ------- / -----------------------

- / ------------

----------- / ------------------- /

H!' ' " " " "

------------ /

------------ /

H!' '

Q%2%% %'(4%2%%. "#!

------------------- -----------------------------

------------------- ----------------------------- --------------

0'. -% '$% %(:2%% 0'. -% '$% %(:'

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå III Ê ïàðàãðàôó 6 &#'%#'#' &#'%##' )%(,-#!#' %##< -, %' #:7%$' T%:%, 9' #%$2I5

108

F

' #%$2I5 )%9' %

-, %' #:< 7%$'-%(, T%%(!( ' #%$' )1, %

' #%$',!'< %$'

= = > = > >= > =' = ' ='

= '

109

= = = > >

>

H%, $6-:',('%,2I %$,' -1, %''$ %< $' #%",$#$(%$',('. % 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( = = - : %#(' ,#'' ''5 =-: %#(' ,#'' ''5

110

P' '''"#.9'$#'- ) = #$ %( ,#''$ -9(' ' #' )1,-9('.6'5' ?- >#$ %(,#''$-9('

- --------------

- ------------- --- -----------------

- ------ --- -----------------

--- --- --- ---

---

111

= = = > >

>

H%, $6-:',('%,2I %$,' -1, %''$ %< $' #%",$#$(%$',('. % 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( 0'( = = - : %#(' ,#'' ''5 =-: %#(' ,#'' ''5

110

P' '''"#.9'$#'- ) = #$ %( ,#''$ -9(' ' #' )1,-9('.6'5' ?- >#$ %(,#''$-9('

- --------------

- ------------- --- -----------------

- ------ --- -----------------

--- --- --- ---

---

111

8% ,% ," ,# ( # ! -7( ,#< %$# ! 8%,%,",# (#!-< 7(,# %$# ! 92

2 2 2 - -------------------- ---------------- -----------------------

2

2

---------------- ------------ ----------------------- 2

T\,# %$# ! 92 T\,# %$#! H' ?M M-: (- '-MM

--- ---

--- --- --- ---

---

>-1,> =-1,=

> -1, > = -1,=

112

' " ' " '" ' "

2

- 0 % '2('. - )%(,:$%-'( %' #< %$ ' V 9 %#5%# : 7 2I. F ' #%$ 2I5 ' #%$ '25 ',5

#$

+,:" %##$%$ ' -1, %$'

113

8% ,% ," ,# ( # ! -7( ,#< %$# ! 8%,%,",# (#!-< 7(,# %$# ! 92

2 2 2 - -------------------- ---------------- -----------------------

2

2

---------------- ------------ ----------------------- 2

T\,# %$# ! 92 T\,# %$#! H' ?M M-: (- '-MM

--- ---

--- --- --- ---

---

>-1,> =-1,=

> -1, > = -1,=

112

' " ' " '" ' "

2

- 0 % '2('. - )%(,:$%-'( %' #< %$ ' V 9 %#5%# : 7 2I. F ' #%$ 2I5 ' #%$ '25 ',5

#$

+,:" %##$%$ ' -1, %$'

113

Ê ïàðàãðàôó 7

%-'(

---

--- %-'(

%-'( %-'( %-'( --- %-'(

------ ---

-----------------------------

- ------- --- --- --- --- --------------------------

- --- --- --- --- ------------------------------

---

--- ---

3

--- --- --- --- ---

! ! !

---

---

------ ------ --------------------------------------------

---

- ------ --- --- --- --- ----

----------------------------------------------------

114

- ' ( --- '( ------ '( --- '( ----

115

Ê ïàðàãðàôó 7

%-'(

---

--- %-'(

%-'( %-'( %-'( --- %-'(

------ ---

-----------------------------

- ------- --- --- --- --- --------------------------

- --- --- --- --- ------------------------------

---

--- ---

3

--- --- --- --- ---

! ! !

---

---

------ ------ --------------------------------------------

---

- ------ --- --- --- --- ----

----------------------------------------------------

114

- ' ( --- '( ------ '( --- '( ----

115

--- ---

- ------ --- --- --- ----

--- ---

--- ---

- --- ----

- --- --- -------

- ------ --- --- ----

! !

--- ---

6 7 F 7-'9"I, = = = > > >

116

)%(, % -'9 "I, I,'2 F "-'9"I, -%(,-1,#$",-'< 9("I,4(#%, )%(, % -'9 "I, I,'2 F " # ' -'< 9"I,!%: '%, $ < $-'9"I,-:.6 == >>

>> >>

Ê ïàðàãðàôó 8 ---

--- ------

–

--- ------ --------------- ------ ------

–

--- --------- --- --------- --------------------- --------- ---------

--- ---------

- ----------–

- ----------- --- ------------ --------------------------

- ---- – ------ ------ ------ ------ ------------------ – --------- ------

------ --------- ------ ------

–

------ ------ --------------------- --------- ---------

------ ------------ ---------

– - – ---------------- --------- - ------------ -----------------------------

– - ------ --------- ----------------------------- ------------

–

------ --------- ------------------------- ------------ = ------------ ------ ---------

F '

117

--- ---

- ------ --- --- --- ----

--- ---

--- ---

- --- ----

- --- --- -------

- ------ --- --- ----

! !

--- ---

6 7 F 7-'9"I, = = = > > >

116

)%(, % -'9 "I, I,'2 F "-'9"I, -%(,-1,#$",-'< 9("I,4(#%, )%(, % -'9 "I, I,'2 F " # ' -'< 9"I,!%: '%, $ < $-'9"I,-:.6 == >>

>> >>

Ê ïàðàãðàôó 8 ---

--- ------

–

--- ------ --------------- ------ ------

–

--- --------- --- --------- --------------------- --------- ---------

--- ---------

- ----------–

- ----------- --- ------------ --------------------------

- ---- – ------ ------ ------ ------ ------------------ – --------- ------

------ --------- ------ ------

–

------ ------ --------------------- --------- ---------

------ ------------ ---------

– - – ---------------- --------- - ------------ -----------------------------

– - ------ --------- ----------------------------- ------------

–

------ --------- ------------------------- ------------ = ------------ ------ ---------

F '

117

---

------

Ã ë à â à IV

F '

MMM M>

ÌÍÎÃÎ×ËÅÍÛ

- ----

N%$.6 M M > N%.6 M ] > N.%$ '.6 M M > ---

--- – --- ------ ------------------ – ----- ------

– ------ ------ ------ ------ ------------------ – ------ ------

+

--- ------ ------------ ------

– ---- ---- ----

------------------ ------ ------ - ------ Q%:'.-"4'%%".6 ---- - Q%:'$-"4'%(%,. ----

– + –– --------------- ------------------------- ---------------

+ – – – – - --------------- ------------------------- --------------- -------------

– – -------------------------- -------------- ------- / – – - / ---------------------------------- ------------ ----------

-------

----------- ------

)#!' '

/ T!' %:',:-"4'%(!'$ ! - -------

- % &% ' %% %'% $ -------

118

§ 9. Ñóììà è ðàçíîñòü ìíîãî÷ëåíîâ 24. Ìíîãî÷ëåí è åãî ñòàíäàðòíûé âèä

0 ' #5%-'

0 '(5%-'

'-#5%-' 0 '',#5%-'%#'.5 ' '.(5%-' '#5%-' '.-#5%-'

' ' ' ' ' '' '

119

---

------

Ã ë à â à IV

F '

MMM M>

ÌÍÎÃÎ×ËÅÍÛ

- ----

N%$.6 M M > N%.6 M ] > N.%$ '.6 M M > ---

--- – --- ------ ------------------ – ----- ------

– ------ ------ ------ ------ ------------------ – ------ ------

+

--- ------ ------------ ------

– ---- ---- ----

------------------ ------ ------ - ------ Q%:'.-"4'%%".6 ---- - Q%:'$-"4'%(%,. ----

– + –– --------------- ------------------------- ---------------

+ – – – – - --------------- ------------------------- --------------- -------------

– – -------------------------- -------------- ------- / – – - / ---------------------------------- ------------ ----------

-------

----------- ------

)#!' '

/ T!' %:',:-"4'%(!'$ ! - -------

- % &% ' %% %'% $ -------

118

§ 9. Ñóììà è ðàçíîñòü ìíîãî÷ëåíîâ 24. Ìíîãî÷ëåí è åãî ñòàíäàðòíûé âèä

0 ' #5%-'

0 '(5%-'

'-#5%-' 0 '',#5%-'%#'.5 ' '.(5%-' '#5%-' '.-#5%-'

' ' ' ' ' '' '

119

F -: =-: ' %,7%#, " !' '$ - !' ' '" '#'2(' -: -: !' = -:.6!' '$6

[-'( [-'(

[-'( [-'(

[-'( [-'(

?- ?-

120

- ------ --------- --- ----

--- --- --- ---

–

– - --- --- --- -------------- --------- --- -----

- ------------------------ ---------------- ------ --- -----------------

- ---------------- ------ -----------

- ------------------------ ------------------- --- --------------

) I,'2$-'!' ' ) I,'2$-'!' '

25. Ñëîæåíèå è âû÷èòàíèå ìíîãî÷ëåíîâ

121

F -: =-: ' %,7%#, " !' '$ - !' ' '" '#'2(' -: -: !' = -:.6!' '$6

[-'( [-'(

[-'( [-'(

[-'( [-'(

?- ?-

120

- ------ --------- --- ----

--- --- --- ---

–

– - --- --- --- -------------- --------- --- -----

- ------------------------ ---------------- ------ --- -----------------

- ---------------- ------ -----------

- ------------------------ ------------------- --- --------------

) I,'2$-'!' ' ) I,'2$-'!' '

25. Ñëîæåíèå è âû÷èòàíèå ìíîãî÷ëåíîâ

121

: !! ! !

5

5 5

122

5 5 5 5 5

---

---

-:!' ' = -:!' '

123

: !! ! !

5

5 5

122

5 5 5 5 5

---

---

-:!' ' = -:!' '

123

N#, '

?-#''.66# N#, '

---

---

), ''#.9''!#% 1-< ''$#'%,%#, ! ---

– ------

124

---

-

–---------–

''$%,-''#% )"I, M MMM – - ----------- / -----------------------------

--- --- --- --- --- ---

---

--- ---

---

---

125

N#, '

?-#''.66# N#, '

---

---

), ''#.9''!#% 1-< ''$#'%,%#, ! ---

– ------

124

---

-

–---------–

''$%,-''#% )"I, M MMM – - ----------- / -----------------------------

--- --- --- --- --- ---

---

--- ---

---

---

125

---

--- ---

---

'( '( '((' ('( '(

---

--- --- --- --- --- --- ---

---

--- ---

---

---

--- --- ---

--- ---

126

---

' ' '' ' ' '

---

1 1

--- --- ---

26. Óìíîæåíèå îäíî÷ëåíà íà ìíîãî÷ëåí

§ 10. Ïðîèçâåäåíèå îäíî÷ëåíà è ìíîãî÷ëåíà

127

---

--- ---

---

'( '( '((' ('( '(

---

--- --- --- --- --- --- ---

---

--- ---

---

---

--- --- ---

--- ---

126

---

' ' '' ' ' '

---

1 1

--- --- ---

26. Óìíîæåíèå îäíî÷ëåíà íà ìíîãî÷ëåí

§ 10. Ïðîèçâåäåíèå îäíî÷ëåíà è ìíîãî÷ëåíà

127

--- --- --- --- S S )7(#%5I",. )7(3 % )7(33 % )7(#%5 I",.#'%,-75 %5%< %#$:76

128

-''-9('.!' '$-: >-1, >-:

- ----

1 1

129

--- --- --- --- S S )7(#%5I",. )7(3 % )7(33 % )7(#%5 I",.#'%,-75 %5%< %#$:76

128

-''-9('.!' '$-: >-1, >-:

- ----

1 1

129

---

---

------ ! !

! !

----------- -----------

------ --------

------- -------

------------ ------------

130

– – ---------------- ------------

---

– - --- --------------

------ ---

– – - ---------------- -----------

---

– - --- ---------------

---

------ ---

------ -------- --------

! ! ---

------ ------

+ – ------------------- -------------------

------ ! !

---

– – ---------------- ----------------

-------- ---

--- ---

-------- --------

--- ---

------ --- ---

------------- ---------- --------

-------- ----- ---

------

+ + ---------------- ------------

--- ---

'+ – ---------------- ------------- ' '

''' ''' '

' --- ' ---

131

---

---

------ ! !

! !

----------- -----------

------ --------

------- -------

------------ ------------

130

– – ---------------- ------------

---

– - --- --------------

------ ---

– – - ---------------- -----------

---

– - --- ---------------

---

------ ---

------ -------- --------

! ! ---

------ ------

+ – ------------------- -------------------

------ ! !

---

– – ---------------- ----------------

-------- ---

--- ---

-------- --------

--- ---

------ --- ---

------------- ---------- --------

-------- ----- ---

------

+ + ---------------- ------------

--- ---

'+ – ---------------- ------------- ' '

''' ''' '

' --- ' ---

131

– ---------------- --- -----

–

– ------------------- ------------

---

+ – --------------- --- ------------

' + – ---------------- ---------------- '

– – - ------------ -----------

– + - ------- ------------ --- --------------

+ – --------------------- ------------ ----------------- -----------

------

+ – --------------------- ------------

---

– + --------------------- ---------- ------------

+ – + - ----------- ---------- -----------

---

---

–

+ - ---------------- --------------

– – ---------------- ----------------

132

– – - ----------------- ----------------

– – --------------- ------------ --

'' ''

' ' ' + – - ------------------- --- --------------

------ ---

),%( 0%%(#"'% . 0 +%#,#'' '#% ' 0 .0 ),%( ($ %' % " #$ % -#$ % P'$ -#'%%%#,#'' S'.,"('#'. % ),%(#3'(-' #330 #333'(0 --- #%" ! '$ -

--- - ,%#: #' +%#

,#'' + - --- -----------------------

---

# 3 '( - #75 # 33 0 # 333 0

133

– ---------------- --- -----

–

– ------------------- ------------

---

+ – --------------- --- ------------

' + – ---------------- ---------------- '

– – - ------------ -----------

– + - ------- ------------ --- --------------

+ – --------------------- ------------ ----------------- -----------

------

+ – --------------------- ------------

---

– + --------------------- ---------- ------------

+ – + - ----------- ---------- -----------

---

---

–

+ - ---------------- --------------

– – ---------------- ----------------

132

– – - ----------------- ----------------

– – --------------- ------------ --

'' ''

' ' ' + – - ------------------- --- --------------

------ ---

),%( 0%%(#"'% . 0 +%#,#'' '#% ' 0 .0 ),%( ($ %' % " #$ % -#$ % P'$ -#'%%%#,#'' S'.,"('#'. % ),%(#3'(-' #330 #333'(0 --- #%" ! '$ -

--- - ,%#: #' +%#

,#'' + - --- -----------------------

---

# 3 '( - #75 # 33 0 # 333 0

133

),%(#33%. %'"#3 0 H3%< %( #33% P'$ #33!< %( --- " %%(#3 %%%#,#'' ---

#3% %'#33 0 ),%(-'(9'. #( 5 # %''% #( # % N'#'$ '#' +%#,#'' (9'. #(-' 5#'( ),%(-7(," """9'.!< - '5! ------ '5 ''('(< ( ----

4 -'#%(-1, -------- --------

-7(,"#'" ),%( ' %'2 +-%' 9' . - '-"! --------- ' ' -"(! -------

''(4 +%#,#'' --------- ---------

'%'2 ),%(%%$'-# "'-,(-#< ' '.5 -,( --- ' --- ! ' ------

(4 +%#,#'' ------------ -------- ------------

- D2%!9#$-6 -6"! ----

%%$'#' +%#,#'' + -------- ---------------------

T!' % %%$' ! H%-%

#% -!4'%%$'% ),%("#$4'!'-,(#% " ",!#$ 0 ),(#% $"#5 4'. $ ",!#5 0 +%# ,#''

#% -!5'%%$'% F -% '$ F -% '$ 333Z #( 3333 #(

3333Z #( 33333Z #(

y y = x2

B 1

F -% '$ %"

–2

-#%''%%$' !.

134

y=4

4 A

135

0 1 2

x

),%(#33%. %'"#3 0 H3%< %( #33% P'$ #33!< %( --- " %%(#3 %%%#,#'' ---

#3% %'#33 0 ),%(-'(9'. #( 5 # %''% #( # % N'#'$ '#' +%#,#'' (9'. #(-' 5#'( ),%(-7(," """9'.!< - '5! ------ '5 ''('(< ( ----

4 -'#%(-1, -------- --------

-7(,"#'" ),%( ' %'2 +-%' 9' . - '-"! --------- ' ' -"(! -------

''(4 +%#,#'' --------- ---------

'%'2 ),%(%%$'-# "'-,(-#< ' '.5 -,( --- ' --- ! ' ------

(4 +%#,#'' ------------ -------- ------------

- D2%!9#$-6 -6"! ----

%%$'#' +%#,#'' + -------- ---------------------

T!' % %%$' ! H%-%

#% -!4'%%$'% ),%("#$4'!'-,(#% " ",!#$ 0 ),(#% $"#5 4'. $ ",!#5 0 +%# ,#''

#% -!5'%%$'% F -% '$ F -% '$ 333Z #( 3333 #(

3333Z #( 33333Z #(

y y = x2

B 1

F -% '$ %"

–2

-#%''%%$' !.

134

y=4

4 A

135

0 1 2

x

' '' '

y y = x2

B 1

F -% '$ %"

y = 2x

1 0 A 2

x

---

---

--- ---

27. Âûíåñåíèå îáùåãî ìíîæèòåëÿ çà ñêîáêè ' ' ' '

'('('('(

136

---

- ---- ---

---

---

---

- ----

---

---

--- ---

137

' '' '

y y = x2

B 1

F -% '$ %"

y = 2x

1 0 A 2

x

---

---

--- ---

27. Âûíåñåíèå îáùåãî ìíîæèòåëÿ çà ñêîáêè ' ' ' '

'('('('(

136

---

- ---- ---

---

---

---

- ----

---

---

--- ---

137

T'!'95'%#('-!#< ''

)!#' %$ ' -1, '' #.9' %$'

138

T75'9( T75'9(

T75'9( '' T75'9('

''' ' ' '' ' T75'9( T75'9(

139

T'!'95'%#('-!#< ''

)!#' %$ ' -1, '' #.9' %$'

138

T75'9( T75'9(

T75'9( '' T75'9('

''' ' ' '' ' T75'9( T75'9(

139

' (' ' ( ),%(%%$'%"#' "#$'-,(%" - '#' ------ P'$ ''.5 ,#' ----

-,(! '' --- '(4%%#,#''

------ ------ ---

%%$'%"#'

+ – ------------------- -------------------

------ --- ---

–

- ----------- -----------

–

140

28. Óìíîæåíèå ìíîãî÷ëåíà íà ìíîãî÷ëåí '''

– – ---------------- -------------------

§ 11. Ïðîèçâåäåíèå ìíîãî÷ëåíîâ

)7(I",.#'%,-75 %5

141

' (' ' ( ),%(%%$'%"#' "#$'-,(%" - '#' ------ P'$ ''.5 ,#' ----

-,(! '' --- '(4%%#,#''

------ ------ ---

%%$'%"#'

+ – ------------------- -------------------

------ --- ---

–

- ----------- -----------

–

140

28. Óìíîæåíèå ìíîãî÷ëåíà íà ìíîãî÷ëåí '''

– – ---------------- -------------------

§ 11. Ïðîèçâåäåíèå ìíîãî÷ëåíîâ

)7(I",.#'%,-75 %5

141

'' ' '' '' ' '' '''''''' '''

3

142

' '' ' ' ' ' ' '

143

'' ' '' '' ' '' '''''''' '''

3

142

' '' ' ' ' ' ' '

143

'' '' ' ' ' ' ' '

144

-: = -:

---

---

145

'' '' ' ' ' ' ' '

144

-: = -:

---

---

145

- ----

---

--- ---

),%( %#'. P'$ #'(4" %' '(4-!#< '$#,6%('.6%%#,#'' % ),%( %#'. )!#'(46 )!#''(46 P'$ !'%( 9, -!#'$ %%# ,#'' %

N'%

J'%

)7(%

K.

+

146

6 P'$ -7(,# %$' %%%#,#'' 4'-$,"('%' % ),%(%'# %"%'.-$,"('< % % )7(# %-< 7(-$,"(' % P'$ -7( # ' % '(4 %%# ,#'' %'# % ),%( " '5 " 9' . < ( '( )'# !' 5 !"# 5 P'$ !"#'' < 5(4%%#,#'' "'5 ),%( " '5 !' 9' . ( '( )'#!' " " F" "9'.#%-6( " – – - --- ---------------- ----------

+ – ---------------- ------------

147

- ----

---

--- ---

),%( %#'. P'$ #'(4" %' '(4-!#< '$#,6%('.6%%#,#'' % ),%( %#'. )!#'(46 )!#''(46 P'$ !'%( 9, -!#'$ %%# ,#'' %

N'%

J'%

)7(%

K.

+

146

6 P'$ -7(,# %$' %%%#,#'' 4'-$,"('%' % ),%(%'# %"%'.-$,"('< % % )7(# %-< 7(-$,"(' % P'$ -7( # ' % '(4 %%# ,#'' %'# % ),%( " '5 " 9' . < ( '( )'# !' 5 !"# 5 P'$ !"#'' < 5(4%%#,#'' "'5 ),%( " '5 !' 9' . ( '( )'#!' " " F" "9'.#%-6( " – – - --- ---------------- ----------

+ – ---------------- ------------

147

+,## % G#%,. % &!'%(,# % G,!'% %

29. Ðàçëîæåíèå ìíîãî÷ëåíà íà ìíîæèòåëè ñïîñîáîì ãðóïïèðîâêè ''' '((''('('( 3

'('(('('(''( '(( ' --- --- --- --- --- --- --- ---

+ - --- ------ ------ --- --- --- --- --- ----------

--- --- --- --- --- ---

------ --- --- ---

--- ---

'''';' ';''

148

149

+,## % G#%,. % &!'%(,# % G,!'% %

29. Ðàçëîæåíèå ìíîãî÷ëåíà íà ìíîæèòåëè ñïîñîáîì ãðóïïèðîâêè ''' '((''('('( 3

'('(('('(''( '(( ' --- --- --- --- --- --- --- ---

+ - --- ------ ------ --- --- --- --- --- ----------

--- --- --- --- --- ---

------ --- --- ---

--- ---

'''';' ';''

148

149

*%#

;5'5#.

H%"#'(

K.

+

P'$ 9'#' % -, ( ' (4%%#,#'' %# ),%("9'!"##( !5# %" '#'!' !5 K"-!## % !5!"#! %# !5 K"#.-'-''/ %%#$ 5 "9'!"##(!5#'(

---

---

30. Äîêàçàòåëüñòâî òîæäåñòâ

150

! ! ! ! ! ! ! !

$ $ $ $

151

*%#

;5'5#.

H%"#'(

K.

+

P'$ 9'#' % -, ( ' (4%%#,#'' %# ),%("9'!"##( !5# %" '#'!' !5 K"-!## % !5!"#! %# !5 K"#.-'-''/ %%#$ 5 "9'!"##(!5#'(

---

---

30. Äîêàçàòåëüñòâî òîæäåñòâ

150

! ! ! ! ! ! ! !

$ $ $ $

151

&#'%#'$#$%$9%#

&#'%#'$#$%$9%# &#'%#'$#$%$9%#

&#'%#'$#$%$9%#

152

- --- --- --- ----

---

- ----

---

– + ---------------- ---------------

)!' '-#"#.9'$''(4!' < '$#" – – --------------- ---------------

) %,5#'

=0#' >0''-- = =0'-

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå IV Ê ïàðàãðàôó 9 ---

--- --- --- --- --- --- --- --- ---

+

- ------ –------------------

153

&#'%#'$#$%$9%#

&#'%#'$#$%$9%# &#'%#'$#$%$9%#

&#'%#'$#$%$9%#

152

- --- --- --- ----

---

- ----

---

– + ---------------- ---------------

)!' '-#"#.9'$''(4!' < '$#" – – --------------- ---------------

) %,5#'

=0#' >0''-- = =0'-

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå IV Ê ïàðàãðàôó 9 ---

--- --- --- --- --- --- --- --- ---

+

- ------ –------------------

153

--- --- ---

---

– ! ! ! ! ! ! ! ! ! --- --- --- ---

---

---

):2 #.9'$ '. % ' ' +,:" %# '.6 %'" ' '"#%"' ' F62.6 ' 8% ' ' - '.6 #.9' #%" ' 8% ' ' ' %$ ' ' ' *% '%,#,6' '.6 % #%"$#$%$ '. %-1,-' '.6 #.< 9'9 ' F62.6 '

154

%"# #"% %"##"%-,!''.6!' '$6%"#

--- --- --- --- ---

--- ---

--- --- ---

-: -: -:

155

--- --- ---

---

– ! ! ! ! ! ! ! ! ! --- --- --- ---

---

---

):2 #.9'$ '. % ' ' +,:" %# '.6 %'" ' '"#%"' ' F62.6 ' 8% ' ' - '.6 #.9' #%" ' 8% ' ' ' %$ ' ' ' *% '%,#,6' '.6 % #%"$#$%$ '. %-1,-' '.6 #.< 9'9 ' F62.6 '

154

%"# #"% %"##"%-,!''.6!' '$6%"#

--- --- --- --- ---

--- ---

--- --- ---

-: -: -:

155

--- --- --- ---

--- --- --- ---

-: -: > -:

--- --- --- --- --- ---

--- --- --- --- --- ---

--- ---

--- --- ---

),%( 1II2'--2'('%"%. %#'. P'$!'%(9,#,$-< %'#,$-#. %%%#,#''

%

156

),%(' % 8%',--%(%-#2I, -, %#' +%##,#'' ' % ),%(' % 8%',--%(%#2I, ',# %$' +%#,#''

' % ),%(-#.#2I.''" %%%#$: % F"'' %#' -, ''#' +%#,#'' ' %

Ê ïàðàãðàôó 10

--- --- --- --- --- ---

),%(!,' % )-%(',0!' ,< '9("' +%#,#'' !,' %

--- --- ---

157

--- --- --- ---

--- --- --- ---

-: -: > -:

--- --- --- --- --- ---

--- --- --- --- --- ---

--- ---

--- --- ---

),%( 1II2'--2'('%"%. %#'. P'$!'%(9,#,$-< %'#,$-#. %%%#,#''

%

156

),%(' % 8%',--%(%-#2I, -, %#' +%##,#'' ' % ),%(' % 8%',--%(%#2I, ',# %$' +%#,#''

' % ),%(-#.#2I.''" %%%#$: % F"'' %#' -, ''#' +%#,#'' ' %

Ê ïàðàãðàôó 10

--- --- --- --- --- ---

),%(!,' % )-%(',0!' ,< '9("' +%#,#'' !,' %

--- --- ---

157

#330 " F#3"%#< %%(# !(4 #33

#3",-#! " %##33 0 "

-: = -: ---

-:

>

-: ' ---

-:

--- ---

---

---

--- --- ---

– – +

--------------------- ------------------- ------------------------

),%(#33%!#! #%"#3%!#! #% H3% ! %%( #33%%%( P'$ #33% %%(' '(4%%#,#'' #33%!#! #3 0 ),%( # 3 ", -#! " %# " # 33 0 " *! #3"%%( "

158

+

L!5#8

--

---

L!8#5

--- --- ---

- ------ ------ ------ --- --- --------------------

+

- -------- ------------ ------ -- -----

&:

P'$ -,(9,-%'$#' %%# ,#''

+

– + – + + ---------------- ------------------- ------------ --------------------- ------------------------ ------------------

,@

– +

– - ------------------- ------------------- ---------------

F-6

--- '

#% -!5 ! '

,:@

&:

+:

3-6

33-6

--

---

),(-5''.5-6'9 ---

--- --- --- --- ---

#5-6"'-#.5 ! '%< %$' %

159

#330 " F#3"%#< %%(# !(4 #33

#3",-#! " %##33 0 "

-: = -: ---

-:

>

-: ' ---

-:

--- ---

---

---

--- --- ---

– – +

--------------------- ------------------- ------------------------

),%(#33%!#! #%"#3%!#! #% H3% ! %%( #33%%%( P'$ #33% %%(' '(4%%#,#'' #33%!#! #3 0 ),%( # 3 ", -#! " %# " # 33 0 " *! #3"%%( "

158

+

L!5#8

--

---

L!8#5

--- --- ---

- ------ ------ ------ --- --- --------------------

+

- -------- ------------ ------ -- -----

&:

P'$ -,(9,-%'$#' %%# ,#''

+

– + – + + ---------------- ------------------- ------------ --------------------- ------------------------ ------------------

,@

– +

– - ------------------- ------------------- ---------------

F-6

--- '

#% -!5 ! '

,:@

&:

+:

3-6

33-6

--

---

),(-5''.5-6'9 ---

--- --- --- --- ---

#5-6"'-#.5 ! '%< %$' %

159

,:@

&

+:

3#,%

--

---

33#,%

--

---

P'$ 3#,%'6%$"'%%$'#'

P'$ %%$' - ': # ! (4 -#%%#,#'' %%(#%$ 5# @ ),%( @ 0%%( '$ ,:@

&:

+:

--- %%$'$%"%%#,#''

) ':

--- --- --- ---

)# '$

------ --- --- --- --- --- ----

- --- ----

------ ---

@

------ ---------

---

%%('"#,% @ ,"" 0@ &%%$' ' ---

),%( @ 0%%(-#"2%"%< %( #" 0 @ )#.5 -6 ---

#5 0 --- - # 1 -,( #6

0%%$'%" +%#,#'' --- ---

@ %%( -#" 2% @ #" 0 @ #% -!4#" ),%( @ 0%%(#%$ 5# ,:@

&:

+:

) ':

)# '$

160

P'$ -,( - ': ' '(4 %%# ,#'' %%( '$ @ ),%(-#9'.#.-,%( % #'( )-',! '59'.#.-,%( % H.-,< %$#'(- % -#!'5#.-,%< % +%#,#'' -#9'.#.-,%(#'(% ),%(-#"%. "-4'2.#"% . )%-#"%%%( #" 0 +%#,#'' -#"%-4'2..#"0 ),%("9'.( '5"-'< #!' " &" '5,< " P'$ %%(,("-, " "9'.,( "

161

,:@

&

+:

3#,%

--

---

33#,%

--

---

P'$ 3#,%'6%$"'%%$'#'

P'$ %%$' - ': # ! (4 -#%%#,#'' %%(#%$ 5# @ ),%( @ 0%%( '$ ,:@

&:

+:

--- %%$'$%"%%#,#''

) ':

--- --- --- ---

)# '$

------ --- --- --- --- --- ----

- --- ----

------ ---

@

------ ---------

---

%%('"#,% @ ,"" 0@ &%%$' ' ---

),%( @ 0%%(-#"2%"%< %( #" 0 @ )#.5 -6 ---

#5 0 --- - # 1 -,( #6

0%%$'%" +%#,#'' --- ---

@ %%( -#" 2% @ #" 0 @ #% -!4#" ),%( @ 0%%(#%$ 5# ,:@

&:

+:

) ':

)# '$

160

P'$ -,( - ': ' '(4 %%# ,#'' %%( '$ @ ),%(-#9'.#.-,%( % #'( )-',! '59'.#.-,%( % H.-,< %$#'(- % -#!'5#.-,%< % +%#,#'' -#9'.#.-,%(#'(% ),%(-#"%. "-4'2.#"% . )%-#"%%%( #" 0 +%#,#'' -#"%-4'2..#"0 ),%("9'.( '5"-'< #!' " &" '5,< " P'$ %%(,("-, " "9'.,( "

161

0%$' ''9(%$' %$' #-!#< ''9(' '9(' ) )

--- --- ---

162

---

------ ---

'''' '' ( ( ( 8% ' ' % 9 ' ' '-<-9',' 8% ' '%9' ' ' -!#'-<-9',, '. % &%%#,!' ' % 8% " 2I. !-%( # ' -$ -, %$ % L6%,#' %$' N$6!' '.6 %'" '$%,#' V %'%$'!%: '%, $"

163

0%$' ''9(%$' %$' #-!#< ''9(' '9(' ) )

--- --- ---

162

---

------ ---

'''' '' ( ( ( 8% ' ' % 9 ' ' '-<-9',' 8% ' '%9' ' ' -!#'-<-9',, '. % &%%#,!' ' % 8% " 2I. !-%( # ' -$ -, %$ % L6%,#' %$' N$6!' '.6 %'" '$%,#' V %'%$'!%: '%, $"

163

$ #%6 ' '$ % 1 % ' %$ ' %$' $#%6' '$%1 %%$' ' %$'

Ê ïàðàãðàôó 11

1 !!!!!!!

164

>

0%$'

165

$ #%6 ' '$ % 1 % ' %$ ' %$' $#%6' '$%1 %%$' ' %$'

Ê ïàðàãðàôó 11

1 !!!!!!!

164

>

0%$'

165

"(( ( ( ) )

),%( %#'. P'$ -!#'-#.6#,6' '(4-!#< '$#,6%,:76%%#,#'' %

),%( %#'. ),%( %#'.

166

),%(%'# %"%'.-$,"(' % )7(# %-7( -$,"(' % P'$ -7( #' %'(4-7-$,"('%< %#,#'' -7(#% ),%( %' # % " %'. -$,"(< ' % )7(# % -< 7(-$,"(' % P'$ -7( # ' % (4 -7 -$,"(' %< %#,#'' % %

0%'.-$,"('

-7(-$,"('#' % 6 ' 4' ),%('-$,"(' "4' -7( )%!''$4'0 ' -7( P'$ -7(,# %$ '%%#,#'' N'-$,"('4' -7(-$,"('#' ),%('-$,"(' %"4' % -7( % )%!''$' %4' % -7( % P'$ -7(,'(4%$' %%%#,#'' %

% -7(-$,"('

%

167

"(( ( ( ) )

),%( %#'. P'$ -!#'-#.6#,6' '(4-!#< '$#,6%,:76%%#,#'' %

),%( %#'. ),%( %#'.

166

),%(%'# %"%'.-$,"(' % )7(# %-7( -$,"(' % P'$ -7( #' %'(4-7-$,"('%< %#,#'' -7(#% ),%( %' # % " %'. -$,"(< ' % )7(# % -< 7(-$,"(' % P'$ -7( # ' % (4 -7 -$,"(' %< %#,#'' % %

0%'.-$,"('

-7(-$,"('#' % 6 ' 4' ),%('-$,"(' "4' -7( )%!''$4'0 ' -7( P'$ -7(,# %$ '%%#,#'' N'-$,"('4' -7(-$,"('#' ),%('-$,"(' %"4' % -7( % )%!''$' %4' % -7( % P'$ -7(,'(4%$' %%%#,#'' %

% -7(-$,"('

%

167

) ) ) ) ) )

'' ''

168

-1, -1, -1, -1,

169

) ) ) ) ) )

'' ''

168

-1, -1, -1, -1,

169

Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß

)7(#%%'5#'-7 # % %'5 ! ,#''5 -7 -$< ,"('-:%-7(#%%'5 ! !( (

§ 12. Êâàäðàò ñóììû è êâàäðàò ðàçíîñòè 31. Âîçâåäåíèå â êâàäðàò ñóììû è ðàçíîñòè äâóõ âûðàæåíèé '(''((

)7(I",.#'%,-75 %5%< %#$:76

170

--- --- ---

- ----

- --- --- -------

--- --- --- ---

- --- --- --- ----

!!!!!

171

Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß

)7(#%%'5#'-7 # % %'5 ! ,#''5 -7 -$< ,"('-:%-7(#%%'5 ! !( (

§ 12. Êâàäðàò ñóììû è êâàäðàò ðàçíîñòè 31. Âîçâåäåíèå â êâàäðàò ñóììû è ðàçíîñòè äâóõ âûðàæåíèé '(''((

)7(I",.#'%,-75 %5%< %#$:76

170

--- --- ---

- ----

- --- --- -------

--- --- --- ---

- --- --- --- ----

!!!!!

171

MMMM Q%:'$ -"4'%( #' '%('$ ----------------- ------------

--- '( --- ' --- '((

Q%:'$ -"4'%( #' '%('$

------ ''(( --- ''((

-----------------

Q%:'$ -"4'%( #' '%('$

-----------------

@ Q%:'$ -"4'%( #' '%('$ -----------------------

Q%:'$ -"4'%( #' '%('$

-----------------

- ------ ------ ----

Q%:'$ -"4'%( #' '%('$

- --- --------

-----------------------

'(''(( ''((

172

'(''(( ''((

--- --- --- ---

173

MMMM Q%:'$ -"4'%( #' '%('$ ----------------- ------------

--- '( --- ' --- '((

Q%:'$ -"4'%( #' '%('$

------ ''(( --- ''((

-----------------

Q%:'$ -"4'%( #' '%('$

-----------------

@ Q%:'$ -"4'%( #' '%('$ -----------------------

Q%:'$ -"4'%( #' '%('$

-----------------

- ------ ------ ----

Q%:'$ -"4'%( #' '%('$

- --- --------

-----------------------

'(''(( ''((

172

'(''(( ''((

--- --- --- ---

173

--- --- --- ---

--- --- ---

- ----

--- --- ---

- ----

--- --- --- ---

- ----

174

) )

175

--- --- --- ---

--- --- ---

- ----

--- --- ---

- ----

--- --- --- ---

- ----

174

) )

175

) )

-

----

-

----

--- ---

176

+,##-!#'5 % % G#%,.-!#'5 % %

177

) )

-

----

-

----

--- ---

176

+,##-!#'5 % % G#%,.-!#'5 % %

177

G#!'%-!#'5 % % &!'%(##-!#'5 % %

1

),%(%%('"-! @ ,"" @ +%(%9'$#' @ ),(-5< ''.5! #' P'$#%(-,(%%#,#'' %%('"-! @ ,""0 @

32. Ðàçëîæåíèå íà ìíîæèòåëè ñ ïîìîùüþ ôîðìóë êâàäðàòà ñóììû è êâàäðàòà ðàçíîñòè !!!

''(('(

1

--- --- ---

---

- --- --- ----

---

178

--- ---

--- ---

^ ^ ^

^'( (^('( '(' ('( %

179

G#!'%-!#'5 % % &!'%(##-!#'5 % %

1

),%(%%('"-! @ ,"" @ +%(%9'$#' @ ),(-5< ''.5! #' P'$#%(-,(%%#,#'' %%('"-! @ ,""0 @

32. Ðàçëîæåíèå íà ìíîæèòåëè ñ ïîìîùüþ ôîðìóë êâàäðàòà ñóììû è êâàäðàòà ðàçíîñòè !!!

''(('(

1

--- --- ---

---

- --- --- ----

---

178

--- ---

--- ---

^ ^ ^

^'( (^('( '(' ('( %

179

--- --- ---

---

=-:.6 = ?#'%# '#' - !' '#.9'$#'

--- --- --- --- --- ---

=

G#!'% &!'%(## )!#'%,.'6!'%(

---

- ------ --- --- --- ------ --- ----

--- ---

0'(!$

! ! '(!$

- --- --- --- ----

- --- --- ----

---

180

---

''''0'(!$

--- --- ---

--- --- --- ---

- ------ -----

181

--- --- ---

---

=-:.6 = ?#'%# '#' - !' '#.9'$#'

--- --- --- --- --- ---

=

G#!'% &!'%(## )!#'%,.'6!'%(

---

- ------ --- --- --- ------ --- ----

--- ---

0'(!$

! ! '(!$

- --- --- --- ----

- --- --- ----

---

180

---

''''0'(!$

--- --- ---

--- --- --- ---

- ------ -----

181

§ 13. Ðàçíîñòü êâàäðàòîâ. Ñóììà è ðàçíîñòü êóáîâ 33. Óìíîæåíèå ðàçíîñòè äâóõ âûðàæåíèé íà èõ ñóììó '('('( ' ' '

'''

)7( -$,"(' % %' #'!'%-75#%%'5#< %%'5

182

--- --- --- --- --- ---

- ------ ----

------ ---

---

---

11 1 1 1

183

§ 13. Ðàçíîñòü êâàäðàòîâ. Ñóììà è ðàçíîñòü êóáîâ 33. Óìíîæåíèå ðàçíîñòè äâóõ âûðàæåíèé íà èõ ñóììó '('('( ' ' '

'''

)7( -$,"(' % %' #'!'%-75#%%'5#< %%'5

182

--- --- --- --- --- ---

- ------ ----

------ ---

---

---

11 1 1 1

183

1 1 1 1 1 11 1 1 1 1 11 1 1 1 ' ' ' ' ' '' ''

1 1

1 1 1 1 1 1

184

11 1 1 ),%( %#'. 1 1 1111

185

1 1 1 1 1 11 1 1 1 1 11 1 1 1 ' ' ' ' ' '' ''

1 1

1 1 1 1 1 1

184

11 1 1 ),%( %#'. 1 1 1111

185

'(( ''('('('( '('('

– - --- ----------

+ + ---------------- -----------

– - --- ----------

– ----------------

+ - ---------------

--- ---

– --------------

),%(%%('"-! @ ,"" @ +%( %9'$ @ ),( -5''.5 ! ,#' P'$#%(-,(%%#,#'' %%('"-! @ ,"" @

186

34. Ðàçëîæåíèå ðàçíîñòè êâàäðàòîâ íà ìíîæèòåëè !!!

<<<< :

187

'(( ''('('('( '('('

– - --- ----------

+ + ---------------- -----------

– - --- ----------

– ----------------

+ - ---------------

--- ---

– --------------

),%(%%('"-! @ ,"" @ +%( %9'$ @ ),( -5''.5 ! ,#' P'$#%(-,(%%#,#'' %%('"-! @ ,"" @

186

34. Ðàçëîæåíèå ðàçíîñòè êâàäðàòîâ íà ìíîæèòåëè !!!

<<<< :

187

--- --- --- ---

--- --- --- --- --- ---

- --- --- --- ----

------ --- ---

------ ' --- ' --- ' --- '

' ( ' ( ' ( ' (

'''

- --------------- ---------------------- -------------------------------------------------- --- – +

–

– – + ------------------------ ---------------------------------------------------- ------------------------- ------ ---

– – + ------------------------ ---------------------------------------------------- ------------------------- ------ --- – +

–

– – + - ---------------------------------------------------- ------------------------- ----------------------–

– +

:

– – + - ---------------------------------------------------- ---------------------- --- ----------------------

–

– +

– – + ------------------------ ---------------------------------------------------- ------------------------- –

– +

' ' ' '

188

189

--- --- --- ---

--- --- --- --- --- ---

- --- --- --- ----

------ --- ---

------ ' --- ' --- ' --- '

' ( ' ( ' ( ' (

'''

- --------------- ---------------------- -------------------------------------------------- --- – +

–

– – + ------------------------ ---------------------------------------------------- ------------------------- ------ ---

– – + ------------------------ ---------------------------------------------------- ------------------------- ------ --- – +

–

– – + - ---------------------------------------------------- ------------------------- ----------------------–

– +

:

– – + - ---------------------------------------------------- ---------------------- --- ----------------------

–

– +

– – + ------------------------ ---------------------------------------------------- ------------------------- –

– +

' ' ' '

188

189

---

--- ---

---

---

--- ---

04'$' =-:

---

---

---

---

04'$' =- :

--- ---

---

190

---

' ' ' ' '' ' '

111

191

---

--- ---

---

---

--- ---

04'$' =-:

---

---

---

---

04'$' =- :

--- ---

---

190

---

' ' ' ' '' ' '

111

191

1 11 '''''' '''''' ''

192

),%( 4' -$,"(' % ' % F"-7('"# %,"" 0 % P'$ -7 :%$'

%%%#,#< ''

% --$,"('#' %

''

- --- --- --- ----

;; ),%(%%$' "#$! '''-,( , #' --- # !#%% %% <

- F" -#'$-!-5 --- --- --- ----

- --- --- --- ----

,%9'-5

35. Ðàçëîæåíèå íà ìíîæèòåëè ñóììû è ðàçíîñòè êóáîâ &&&&

193

1 11 '''''' '''''' ''

192

),%( 4' -$,"(' % ' % F"-7('"# %,"" 0 % P'$ -7 :%$'

%%%#,#< ''

% --$,"('#' %

''

- --- --- --- ----

;; ),%(%%$' "#$! '''-,( , #' --- # !#%% %% <

- F" -#'$-!-5 --- --- --- ----

- --- --- --- ----

,%9'-5

35. Ðàçëîæåíèå íà ìíîæèòåëè ñóììû è ðàçíîñòè êóáîâ &&&&

193

'('(''((

'''''

--- ---

--- --- --- ---

--- --- --- --- --- ---

- --- ----

- --- --- --- --- ----

- --- --- ----

- --------- --- --- ---- - ------ --- --- --- ----

--- ' --- ' --- ' --- ' --- '

0%$' 0%$'

--- --- --- --- ---

' ''''

194

0%$'

0%$' :

195

'('(''((

'''''

--- ---

--- --- --- ---

--- --- --- --- --- ---

- --- ----

- --- --- --- --- ----

- --- --- ----

- --------- --- --- ---- - ------ --- --- --- ----

--- ' --- ' --- ' --- ' --- '

0%$' 0%$'

--- --- --- --- ---

' ''''

194

0%$'

0%$' :

195

&#'%#'$#$%$9%# &#'%#'$#$%$9%#

§ 14. Ïðåîáðàçîâàíèå öåëûõ âûðàæåíèé 36. Ïðåîáðàçîâàíèå öåëîãî âûðàæåíèÿ â ìíîãî÷ëåí _.

– ---------------

---

196

S

197

&#'%#'$#$%$9%# &#'%#'$#$%$9%#

§ 14. Ïðåîáðàçîâàíèå öåëûõ âûðàæåíèé 36. Ïðåîáðàçîâàíèå öåëîãî âûðàæåíèÿ â ìíîãî÷ëåí _.

– ---------------

---

196

S

197

--- --- ---

--- --- --- ---

--- --- --- ---

) --- ---

---

)

198

F9%# #' F9%##'

0'#!9'

--- S ---

------ ---

---

0'#!< 9'

--- --- ---

S ),%(%%$' "'-,(%'2! < - ''.5-,(0 ------ P'$ ''.5 ' ----

-,(! '' (4%%#,#'' -------- --------

%%$'#'

199

--- --- ---

--- --- --- ---

--- --- --- ---

) --- ---

---

)

198

F9%# #' F9%##'

0'#!9'

--- S ---

------ ---

---

0'#!< 9'

--- --- ---

S ),%(%%$' "'-,(%'2! < - ''.5-,(0 ------ P'$ ''.5 ' ----

-,(! '' (4%%#,#'' -------- --------

%%$'#'

199

' --- ' ---

),%( %%( %#$!'" ! % # " @ ' 0 @ &%%$'9,%" ---

F" --- ---

--- --- ---

-------- -------- ---

- --- ----

%#$!'54%%%(:@

37. Ïðèìåíåíèå ðàçëè÷íûõ ñïîñîáîâ äëÿ ðàçëîæåíèÿ íà ìíîæèòåëè

' ' ''

200

'''''' '('(''(('(

201

' --- ' ---

),%( %%( %#$!'" ! % # " @ ' 0 @ &%%$'9,%" ---

F" --- ---

--- --- ---

-------- -------- ---

- --- ----

%#$!'54%%%(:@

37. Ïðèìåíåíèå ðàçëè÷íûõ ñïîñîáîâ äëÿ ðàçëîæåíèÿ íà ìíîæèòåëè

' ' ''

200

'''''' '('(''(('(

201

' ' ' ' ' '' '' '''' '''''

202

= -:.6 ), -!#' 6 -%#('.6 % ' ' ! #,6 -%#('.6 % ' $!(' ' ! 6 0 ' $!(' %$'

203

' ' ' ' ' '' '' '''' '''''

202

= -:.6 ), -!#' 6 -%#('.6 % ' ' ! #,6 -%#('.6 % ' $!(' ' ! 6 0 ' $!(' %$'

203

),%( %#'. 0%$' ) ) =

F % -'9"I, "

F "'-'9"I, #

F #-'9"I,

y

5

x

204

1 1 0 2

1 0 1

x

1 0 1

5 x –9

> = = 0''$%,'%$' -''#% V %'%$' -'' #%

4 1 0 1

y

y

= = = ! ! ! =

y

38. Ïðèìåíåíèå ïðåîáðàçîâàíèé öåëûõ âûðàæåíèé

G'. -% '$"I% %(:'0 %%(:%2%%0

- -----

x

P' ' -, ''" #.9'$ ' %$ ' -''#%

205

),%( %#'. 0%$' ) ) =

F % -'9"I, "

F "'-'9"I, #

F #-'9"I,

y

5

x

204

1 1 0 2

1 0 1

x

1 0 1

5 x –9

> = = 0''$%,'%$' -''#% V %'%$' -'' #%

4 1 0 1

y

y

= = = ! ! ! =

y

38. Ïðèìåíåíèå ïðåîáðàçîâàíèé öåëûõ âûðàæåíèé

G'. -% '$"I% %(:'0 %%(:%2%%0

- -----

x

P' ' -, ''" #.9'$ ' %$ ' -''#%

205

- --- ---

--- --- --- --- --- --- ---

- ---

---

--- --- --- ---

- --- ------ ------ ------ --- -------- ------

;'

;' ---

-----

- --- ----

- --- --- ----

;'-(!#(%$#.#.9'

$

`,.:# %#(''. '5'.I,'2 WII,'25-%:%$

0'. -% '$

206

y = –x + 6

y

y = x2

A

B 1

0 1 –2

x

= >0 -% '$ ;;; ;

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå V Ê ïàðàãðàôó 12

--- ---

------

---

--- ---

--- ---

207

- --- ---

--- --- --- --- --- --- ---

- ---

---

--- --- --- ---

- --- ------ ------ ------ --- -------- ------

;'

;' ---

-----

- --- ----

- --- --- ----

;'-(!#(%$#.#.9'

$

`,.:# %#(''. '5'.I,'2 WII,'25-%:%$

0'. -% '$

206

y = –x + 6

y

y = x2

A

B 1

0 1 –2

x

= >0 -% '$ ;;; ;

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå V Ê ïàðàãðàôó 12

--- ---

------

---

--- ---

--- ---

207

:

- --- --- --- ----

'('('('( '(

- --- ------ --- --- ----

- --- --- --- --- ----

- --- ------ ---

--- ----

--- --- ---

- ---- ---

;

Ê ïàðàãðàôó 13

208

209

:

- --- --- --- ----

'('('('( '(

- --- ------ --- --- ----

- --- --- --- --- ----

- --- ------ ---

--- ----

--- --- ---

- ---- ---

;

Ê ïàðàãðàôó 13

208

209

--- --- --- --- ---

-

------ ----

--- --- --- ---

------ ----

------ --- --- --- --- ---

– + - ------ ---------------------

210

,#''7%$#9%# -#%6 '('('('( '('' (

211

--- --- --- --- ---

-

------ ----

--- --- --- ---

------ ----

------ --- --- --- --- ---

– + - ------ ---------------------

210

,#''7%$#9%# -#%6 '('('('( '('' (

211

' '' '' ' ''

--- --- --- --- --- --- --- ---

- ------ ------ --- --- --- ---

--- ----

–

– + ------------------------ ---------------------------------------------------- ---------------------- ------ – + –

– – + - ----------------------------------------------------------------------- ---------------------- --- --------------------------------

–

– +

– – + - ------------------------------------------------------------------------- ------------------------------- ------ -------------------------------- –

–

'( '( '(

------ --- --- --- --- ---

212

213

' '' '' ' ''

--- --- --- --- --- --- --- ---

- ------ ------ --- --- --- ---

--- ----

–

– + ------------------------ ---------------------------------------------------- ---------------------- ------ – + –

– – + - ----------------------------------------------------------------------- ---------------------- --- --------------------------------

–

– +

– – + - ------------------------------------------------------------------------- ------------------------------- ------ -------------------------------- –

–

'( '( '(

------ --- --- --- --- ---

212

213

)

33

)

' ' ''

------ --- --- ------ ---

- --- --- ----

--- --- ---

------ ---

--- --- --- ------ ---------

0< %$'

------ --- ---

0%$' 0%$' 0%$'

214

Ê ïàðàãðàôó 14

215

)

33

)

' ' ''

------ --- --- ------ ---

- --- --- ----

--- --- ---

------ ---

--- --- --- ------ ---------

0< %$'

------ --- ---

0%$' 0%$' 0%$'

214

Ê ïàðàãðàôó 14

215

---

`,'2$# '5'$ %

F %-'9"I, "

F "'-'9"I,

)

)!,#,: %(#'%# ), -#,: %(#'%# )!,#,: %(#'%#

)

), -#,: %(#'%#

216

217

---

`,'2$# '5'$ %

F %-'9"I, "

F "'-'9"I,

)

)!,#,: %(#'%# ), -#,: %(#'%# )!,#,: %(#'%#

)

), -#,: %(#'%#

216

217

'''''' ''' ''''' )'

---

---

---

)!,#,: %(#'%# )!,-#,: %(#'%#

)!,#,: %(#'%# '(2+'2(2'+(+ )!,-#,: %(#'%# '2(+'+(2 '2'2(+(+'+'+(2?2 '2(+'+(2'(2+

)-, '" ''%9 )-, '" ''%9

D'" ''%9 - G1II2'.- #'.%

--- --- --- ---

) ) )

218

219

'''''' ''' ''''' )'

---

---

---

)!,#,: %(#'%# )!,-#,: %(#'%#

)!,#,: %(#'%# '(2+'2(2'+(+ )!,-#,: %(#'%# '2(+'+(2 '2'2(+(+'+'+(2?2 '2(+'+(2'(2+

)-, '" ''%9 )-, '" ''%9

D'" ''%9 - G1II2'.- #'.%

--- --- --- ---

) ) )

218

219

---

- ------ --- --- ----

=-#%6 1'%#'' 4'

--- --- ------

---

220

''' ''

---

---

---

''''' ''

221

---

- ------ --- --- ----

=-#%6 1'%#'' 4'

--- --- ------

---

220

''' ''

---

---

---

''''' ''

221

'''''' ''''''''

222

223

'''''' ''''''''

222

223

Ã ë à â à VI

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ

'9 '9

§ 15. Ëèíåéíûå óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè è èõ ñèñòåìû

9- #.9'#' 9- #.9< '#' 9-#.< 9'#'

39. Ëèíåéíîå óðàâíåíèå ñ äâóìÿ ïåðåìåííûìè

N ? N ?

N ? N N

--- --- 0 %#(' ---

0'%$' -#%"< %$' #'%$

#%( *.#!#%## %' #:7%$' ',9' %#-%'::2I, ,'9(%#4%$ %'%,:7!'',(' % !,(,--%(%-#

224

--- 04',#''$

' '

$#$%$ $#$%$ $#$%$ '$#$%$

225

Ã ë à â à VI

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ

'9 '9

§ 15. Ëèíåéíûå óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè è èõ ñèñòåìû

9- #.9'#' 9- #.9< '#' 9-#.< 9'#'

39. Ëèíåéíîå óðàâíåíèå ñ äâóìÿ ïåðåìåííûìè

N ? N ?

N ? N N

--- --- 0 %#(' ---

0'%$' -#%"< %$' #'%$

#%( *.#!#%## %' #:7%$' ',9' %#-%'::2I, ,'9(%#4%$ %'%,:7!'',(' % !,(,--%(%-#

224

--- 04',#''$

' '

$#$%$ $#$%$ $#$%$ '$#$%$

225

'

3

---

---

40. Ãðàôèê ëèíåéíîãî óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè

@, ,@ @, @, @ --- ,

% " # $

1 %

); )

226

% " # $

' ' '

-'9 -'9 -'9 '-'9

6

y

å) 4

–4

---

227

à) 4 x á)

ä)

â) 1 0 1

ã)

'

3

---

---

40. Ãðàôèê ëèíåéíîãî óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè

@, ,@ @, @, @ --- ,

% " # $

1 %

); )

226

% " # $

' ' '

-'9 -'9 -'9 '-'9

6

y

å) 4

–4

---

227

à) 4 x á)

ä)

â) 1 0 1

ã)

$

$ $ $

$ $$

y â)

à)

– – - --------------- $ --------------

ã)

1 0 1

$ $ )*****+

H333 H33Z

x

$ $ $ + – - ---------------- -------------

á)

á)

228

x â)

1 1 0

à)

ã)

) --- --- ---

y

- ------ ------ --- ) ----

--- ---

41. Ñèñòåìû ëèíåéíûõ óðàâíåíèé ñ äâóìÿ ïåðåìåííûìè

?$#$%$

3

E#$%$

229

$

$ $ $

$ $$

y â)

à)

– – - --------------- $ --------------

ã)

1 0 1

$ $ )*****+

H333 H33Z

x

$ $ $ + – - ---------------- -------------

á)

á)

228

x â)

1 1 0

à)

ã)

) --- --- ---

y

- ------ ------ --- ) ----

--- ---

41. Ñèñòåìû ëèíåéíûõ óðàâíåíèé ñ äâóìÿ ïåðåìåííûìè

?$#$%$

3

E#$%$

229

---

A(–2; 2)

y 1 y = ––x + 3 3 A(3; 2) 1 0 1 y=x–1

6 2 0 –2

---

230

10

---

y=3 –x + 31 – 4 2

6 10 14 18 22 16 20 x y = –x –4 2

x

231

y 3

---

–

x

y 20 18 16 14

1,2

---

x

--- ---

--- ---

D(0; 2)

–

,3 x

1 1 0 y=2 –x + 2 5

–0

y=

y 1 y = ––x + 2 2

1,5

?$#$%$ ?$#$%$ E#$%$

?$#$%$ E#$%$ ?$#$%$

---

=

---

---

10 1

y

@, @, E#$%$ @, ,@ E#$%$ @,

x

A(1; –1,5)

---

A(–2; 2)

y 1 y = ––x + 3 3 A(3; 2) 1 0 1 y=x–1

6 2 0 –2

---

230

10

---

y=3 –x + 31 – 4 2

6 10 14 18 22 16 20 x y = –x –4 2

x

231

y 3

---

–

x

y 20 18 16 14

1,2

---

x

--- ---

--- ---

D(0; 2)

–

,3 x

1 1 0 y=2 –x + 2 5

–0

y=

y 1 y = ––x + 2 2

1,5

?$#$%$ ?$#$%$ E#$%$

?$#$%$ E#$%$ ?$#$%$

---

=

---

---

10 1

y

@, @, E#$%$ @, ,@ E#$%$ @,

x

A(1; –1,5)

---

---

---

---

y

1 0 1

y=1 –x – 3 2 x

A(0; –3)

y = –3 –x – 3 2

--- ---

0

x

;– 1) A( –1

---

---

---

L'4'

--- ---

-

--- -----

L'4'

---

---

---

+ – ---------------- ------------

– + ---------------- ------------

- -----

233

---

L%' ''"4'5

232

L'4'

y = –2 –x – 5 – 3 3

L'4'

1

---

--- ---

y=x

1

y

L'4'

?4'5 L%' ''9%#4'5

L'4'

--- ---

--- ---

---

---

---

---

y

1 0 1

y=1 –x – 3 2 x

A(0; –3)

y = –3 –x – 3 2

--- ---

0

x

;– 1) A( –1

---

---

---

L'4'

--- ---

-

--- -----

L'4'

---

---

---

+ – ---------------- ------------

– + ---------------- ------------

- -----

233

---

L%' ''"4'5

232

L'4'

y = –2 –x – 5 – 3 3

L'4'

1

---

--- ---

y=x

1

y

L'4'

?4'5 L%' ''9%#4'5

L'4'

--- ---

--- ---

– – ---------------- --- --------------------- --------

------ ------

§ 16. Ðåøåíèå ñèñòåì ëèíåéíûõ óðàâíåíèé 42. Ñïîñîá ïîäñòàíîâêè

---

---

---

---

--- ---

234

235

– – ---------------- --- --------------------- --------

------ ------

§ 16. Ðåøåíèå ñèñòåì ëèíåéíûõ óðàâíåíèé 42. Ñïîñîá ïîäñòàíîâêè

---

---

---

---

--- ---

234

235

------ ,, , , ,

'( ' (

@ , @ , @ , @ ,

@ ---

, ---

@ --- ,

, ,

, ---

' ---

--- ((

( '

– , - ,

------------------

--- ((

– , - @ -----------------

@,

---

--- ---

---

--- ------

------

---

------

---

– , ---------------------- ,

236

---

---

' --- (

--- ( (

@, @,

@,

@,

--- ---

--- ((

@ --- ,

'(

'( '( '(

(

--- ---

---

--- , ,

'( '( ' ( ' (

( ( ' '

@ --- ,

, ---

--- ---

@ ---

(( ( (

, ---

– , ------------------- @

237

------ ,, , , ,

'( ' (

@ , @ , @ , @ ,

@ ---

, ---

@ --- ,

, ,

, ---

' ---

--- ((

( '

– , - ,

------------------

--- ((

– , - @ -----------------

@,

---

--- ---

---

--- ------

------

---

------

---

– , ---------------------- ,

236

---

---

' --- (

--- ( (

@, @,

@,

@,

--- ---

--- ((

@ --- ,

'(

'( '( '(

(

--- ---

---

--- , ,

'( '( ' ( ' (

( ( ' '

@ --- ,

, ---

--- ---

@ ---

(( ( (

, ---

– , ------------------- @

237

--- ------

------ ---

------ --------- ------ ---

---

------ --- ------ --- ---

---

------ ------ ---

---

---

------ ------

------ ---

------ ---

--- ---

--- ------

--- --- --- ---

---

238

---

---

---

---

---

---

---

---

--- ---

---

---

---

+ -

--------------+ ----------------

+ - --------------

--- ---

---

---

--- ------

--- ---

------ ---

---

– --- +

----------------------

---

---

239

--- ------

------ ---

------ --------- ------ ---

---

------ --- ------ --- ---

---

------ ------ ---

---

---

------ ------

------ ---

------ ---

--- ---

--- ------

--- --- --- ---

---

238

---

---

---

---

---

---

---

---

--- ---

---

---

---

+ -

--------------+ ----------------

+ - --------------

--- ---

---

---

--- ------

--- ---

------ ---

---

– --- +

----------------------

---

---

239

---

---

---

---

--- ---

--- ---

--- ---

-------- --------

-------- ---

240

--- ---

--- ---

-------- ---

------ ------

------------- --------

---------- ------------

– ------------------- – -------------------

– – -------------------------------

------

------

------

------

+

--------------------- + ----------------------

--- ---

------ ------

+ ----------------------

-------- --------

-------- --------

+ ---------------------

241

---

---

---

---

--- ---

--- ---

--- ---

-------- --------

-------- ---

240

--- ---

--- ---

-------- ---

------ ------

------------- --------

---------- ------------

– ------------------- – -------------------

– – -------------------------------

------

------

------

------

+

--------------------- + ----------------------

--- ---

------ ------

+ ----------------------

-------- --------

-------- --------

+ ---------------------

241

------ ------

------ ------

------------ ------

-------- --------------

--- --- --- ---

------- ------ --- --- ------

--- --- --- --- --- ---

---------- ------ --- --- ------

---------- ------ --- --- ------ ------

--- --- --- --- --- ---

242

=-:!' '

43. Ñïîñîá ñëîæåíèÿ

---

---

--- --- ---

--- --- --- --- ---

--- --- ---

--- --- --- --- ---

--- --- --- --- ---

243

------ ------

------ ------

------------ ------

-------- --------------

--- --- --- ---

------- ------ --- --- ------

--- --- --- --- --- ---

---------- ------ --- --- ------

---------- ------ --- --- ------ ------

--- --- --- --- --- ---

242

=-:!' '

43. Ñïîñîá ñëîæåíèÿ

---

---

--- --- ---

--- --- --- --- ---

--- --- ---

--- --- --- --- ---

--- --- --- --- ---

243

---

---

---

--- --- --- ---

---

---

244

---

--- --- --- --- ---

!

!

! !

! ! ! !

!

@, @, @, @,

@ @ @ , @, ,

245

---

---

---

--- --- --- ---

---

---

244

---

--- --- --- --- ---

!

!

! !

! ! ! !

!

@, @, @, @,

@ @ @ , @, ,

245

@, @, @ ,

@, , , @, @ @ @ , ,

5 8

6 7 % " # $

246

% "

---

---

---

---

--- ---

F -% '$%%$'

WI-6 !

247

@, @, @ ,

@, , , @, @ @ @ , ,

5 8

6 7 % " # $

246

% "

---

---

---

---

--- ---

F -% '$%%$'

WI-6 !

247

--- ---

-------- --------

--- ---

-------- --------

--- ------ --- ------

---

--- @ --- ,

--- ---

------- --------

--- ---

248

------ --- ------ ---

------------ --------

--- ------ --- ------

@, @,

@ @, @, @, @, @ @ , ,

--- @ --------

------ ---

--- ----

------ ---

--- ------

-------- ------

--- , --- a

-------- , --------

@ ,

,@ , ,@

,@ ,@

,@

, ,

@ @

--- ---

-------- --------

249

--- ---

-------- --------

--- ---

-------- --------

--- ------ --- ------

---

--- @ --- ,

--- ---

------- --------

--- ---

248

------ --- ------ ---

------------ --------

--- ------ --- ------

@, @,

@ @, @, @, @, @ @ , ,

--- @ --------

------ ---

--- ----

------ ---

--- ------

-------- ------

--- , --- a

-------- , --------

@ ,

,@ , ,@

,@ ,@

,@

, ,

@ @

--- ---

-------- --------

249

--- --- ---

),%( # I# #.-,7' !5 # $'# 0 !'$ #I##.-,7'' !5(4%< %#,#'' P'$%(!5#.-,7'!#%$2%%# #,#''

-------- -------- --------

---

?4'5 L%' ''9%#4'5

%:'$ -"4'%( #' %:'$-"4'%( %:'$-"4'%(

44. Ðåøåíèå çàäà÷ ñ ïîìîùüþ ñèñòåì óðàâíåíèé

#I# 0!5#$'#0 !5 ),%( ' "' -$ : " " ,"60 P'$ #%""%%#,#'' P'$ ' "' -$ ' " (4-, #,#''

":'"'-$ ),%(",!#.6#5 "#.6 P'$ "< #.64'' '(4%%#,#'' !'$ #%"#$-, #,#''

",!#.6#5 ),%(!,- 4' # P'$ # !,- # ! (4 %%< #,#'' F#%"!,- < #4'-, #,#''

R

),%(' % # F"!'$6%,,%< %#',#'' !'$!'%( 0,< "

%

),%(#$%' %'#' % P'$ %'#''%(4#5%'.%< %#,#''

250

251

4'#

--- --- ---

),%( # I# #.-,7' !5 # $'# 0 !'$ #I##.-,7'' !5(4%< %#,#'' P'$%(!5#.-,7'!#%$2%%# #,#''

-------- -------- --------

---

?4'5 L%' ''9%#4'5

%:'$ -"4'%( #' %:'$-"4'%( %:'$-"4'%(

44. Ðåøåíèå çàäà÷ ñ ïîìîùüþ ñèñòåì óðàâíåíèé

#I# 0!5#$'#0 !5 ),%( ' "' -$ : " " ,"60 P'$ #%""%%#,#'' P'$ ' "' -$ ' " (4-, #,#''

":'"'-$ ),%(",!#.6#5 "#.6 P'$ "< #.64'' '(4%%#,#'' !'$ #%"#$-, #,#''

",!#.6#5 ),%(!,- 4' # P'$ # !,- # ! (4 %%< #,#'' F#%"!,- < #4'-, #,#''

R

),%(' % # F"!'$6%,,%< %#',#'' !'$!'%( 0,< "

%

),%(#$%' %'#' % P'$ %'#''%(4#5%'.%< %#,#''

250

251

4'#

P'$--, #,#''

#$%'#' % ),%( -'%( :'$ "@ -'%( 9!

"@ P'$ -'%( :'$ ' "@ '(4%%#,#'' D%% :'$ " 9! 0

" P'$ #%$%%#'"-, ,#''

-'%(:'$"@ ),%( 0-9'$$,95'%(I$ '#$ ;95'%(,# %(' % " + , % -7(: " %: % , % "%'(4 +%##,#''

'(4%- %"-(0- ),%(%%(4'. @ %%(-! @ P'$ %%( -! (4 %%# ,#''

),('4'0 '-!0 #%"

%%(-!@

252

),%(-# %#' # F"

% ),%( @ 0 %%( -6 - ': @ 0 "%%(-# '$ ), ,#''$

%%(- ': @ -# '$0 @ ),%(%%(.%"#$ @ ''" @ F" 3

%%(-#"#$ @ #" 0 @ ),%(%%(-#",% @ #" 0 @ P'$#$-,(%%#,#'' F-#.5-4'(4#"#%< -, #,#''

%%( -#" ,% @ #" 0 @

253

P'$--, #,#''

#$%'#' % ),%( -'%( :'$ "@ -'%( 9!

"@ P'$ -'%( :'$ ' "@ '(4%%#,#'' D%% :'$ " 9! 0

" P'$ #%$%%#'"-, ,#''

-'%(:'$"@ ),%( 0-9'$$,95'%(I$ '#$ ;95'%(,# %(' % " + , % -7(: " %: % , % "%'(4 +%##,#''

'(4%- %"-(0- ),%(%%(4'. @ %%(-! @ P'$ %%( -! (4 %%# ,#''

),('4'0 '-!0 #%"

%%(-!@

252

),%(-# %#' # F"

% ),%( @ 0 %%( -6 - ': @ 0 "%%(-# '$ ), ,#''$

%%(- ': @ -# '$0 @ ),%(%%(.%"#$ @ ''" @ F" 3

%%(-#"#$ @ #" 0 @ ),%(%%(-#",% @ #" 0 @ P'$#$-,(%%#,#'' F-#.5-4'(4#"#%< -, #,#''

%%( -#" ,% @ #" 0 @

253

),%( @ 0%%(#%$ 5# @ 0 %%( '$ F" -, ,#''$

%%(#%$ 5# @ ),%( %%#''$ %%( -6 @ %%( '$ @ P'$ #$ - ': -# %%# ,#'' P'$#$-,(-# '$- ':-, ,",#''

&4%%, --- --- --- ---

(4 --- ---

--- ---

---

--- ---

% ),%( "@% 0 -'%( 9! "@% 0 -'%( ), ,#''$ &4%%,

3

"@%

),%('3- '"'330 P'$%('" #%"%%#,#''

F-%-%'#'3-'"%'#!

-'%( 9! "@% -'%(

%%#''$ %%( -6

@ +< %( '$ @

''$ --- --- --- ---

),%(' %#',"0 ), ,#<

'3-'"'330'"

254

),%( % ), ,#''$ ---

&4%%,

% ),%( %%$# %'2 "!'$%,< ,2I %%%#,#'' % %<

255

),%( @ 0%%(#%$ 5# @ 0 %%( '$ F" -, ,#''$

%%(#%$ 5# @ ),%( %%#''$ %%( -6 @ %%( '$ @ P'$ #$ - ': -# %%# ,#'' P'$#$-,(-# '$- ':-, ,",#''

&4%%, --- --- --- ---

(4 --- ---

--- ---

---

--- ---

% ),%( "@% 0 -'%( 9! "@% 0 -'%( ), ,#''$ &4%%,

3

"@%

),%('3- '"'330 P'$%('" #%"%%#,#''

F-%-%'#'3-'"%'#!

-'%( 9! "@% -'%(

%%#''$ %%( -6

@ +< %( '$ @

''$ --- --- --- ---

),%(' %#',"0 ), ,#<

'3-'"'330'"

254

),%( % ), ,#''$ ---

&4%%,

% ),%( %%$# %'2 "!'$%,< ,2I %%%#,#'' % %<

255

?# %!-4%$ -%(,' (4#!%6'"

-#' (' % ),%( "!'!. " 0$#. ), ,#''$

&4%%,

!.!'"$#.0" ),%( -#$ " 9' !"#( 5 33 0 #% ' !"#$ 5 - ,%#:#' )#$ " !"# %#6 -' 5 33 0

-1,

-#$"9'!"#(#$0 5

--- --- 0"I%-9'#333Z3 #$6

--- 0"I%-9'#33333Z #$6 > -:

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå VI Ê ïàðàãðàôó 15 0'$#$%$ 0'$#$%$ 0$#$%$ 0$#$%$ @, @, @, @, &%% #.9' - V %%$'2' ' ' '%$-1< ,'-62.6- '9.( 4'''",#''$

' '''''

' '''

256

257

?# %!-4%$ -%(,' (4#!%6'"

-#' (' % ),%( "!'!. " 0$#. ), ,#''$

&4%%,

!.!'"$#.0" ),%( -#$ " 9' !"#( 5 33 0 #% ' !"#$ 5 - ,%#:#' )#$ " !"# %#6 -' 5 33 0

-1,

-#$"9'!"#(#$0 5

--- --- 0"I%-9'#333Z3 #$6

--- 0"I%-9'#33333Z #$6 > -:

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå VI Ê ïàðàãðàôó 15 0'$#$%$ 0'$#$%$ 0$#$%$ 0$#$%$ @, @, @, @, &%% #.9' - V %%$'2' ' ' '%$-1< ,'-62.6- '9.( 4'''",#''$

' '''''

' '''

256

257

)%. %.".--%(#-. (4--,#-.% ,9 - %''. 0'-% 0'-% 0-% 0'-% 0-% 0-% 0'-% 0-% T' ('-, ),%( #,6,#.6 ' 4, -$,#.6 F"

) ) 2.64'5' ) ) 2.64'5' T' (' ),%(#,!' ' %#' F" %:%, -1,

=-:.6-9('.6!' '$6 %: --- ?'-6

2.6 #'%#'#!9' 2 % --- 0'

2

0

0

2

x

–2

#' F 5-'9"I, F 4'-'9"I, #' F "-'9"I,

---

0

1

x

–1

y

0 –1

258

x

y

y

=-#%6 -1,"I'-%%( ) "I-%%( # <

2

%

y

---

259

1

x

)%. %.".--%(#-. (4--,#-.% ,9 - %''. 0'-% 0'-% 0-% 0'-% 0-% 0-% 0'-% 0-% T' ('-, ),%( #,6,#.6 ' 4, -$,#.6 F"

) ) 2.64'5' ) ) 2.64'5' T' (' ),%(#,!' ' %#' F" %:%, -1,

=-:.6-9('.6!' '$6 %: --- ?'-6

2.6 #'%#'#!9' 2 % --- 0'

2

0

0

2

x

–2

#' F 5-'9"I, F 4'-'9"I, #' F "-'9"I,

---

0

1

x

–1

y

0 –1

258

x

y

y

=-#%6 -1,"I'-%%( ) "I-%%( # <

2

%

y

---

259

1

x

8 4 –8 –4 0 –4

WI -%%$ % %(: # % %(:

y

4

8 x

–8

) ':$ ) %2%%:$ WI%%!#,6 -$.6

x

WI%%!#,6 -$.6

y

0

% % > WI %% ! #,6 -,-$< .6

–4 0 –4

4

WI%%!#,6 -$.6

y

x

2 0 –2

–5

260

x

1

x

1

x

y

1 0

x

0#'-$#$%$4'

0

1

4

2

–4

y

M M

y

y

0 –2

WI%%!#,6 -$.6

% = % > )1, "I # #5 -,< -%% 0 -$$ # -#5 0 -$$ " #-,-$.

M M

0-'$#$%$4'

*( . ..)*-

261

8 4 –8 –4 0 –4

WI -%%$ % %(: # % %(:

y

4

8 x

–8

) ':$ ) %2%%:$ WI%%!#,6 -$.6

x

WI%%!#,6 -$.6

y

0

% % > WI %% ! #,6 -,-$< .6

–4 0 –4

4

WI%%!#,6 -$.6

y

x

2 0 –2

–5

260

x

1

x

1

x

y

1 0

x

0#'-$#$%$4'

0

1

4

2

–4

y

M M

y

y

0 –2

WI%%!#,6 -$.6

% = % > )1, "I # #5 -,< -%% 0 -$$ # -#5 0 -$$ " #-,-$.

M M

0-'$#$%$4'

*( . ..)*-

261

?5 ,-% '$-#.6#,6-$.6

)#-6 ! ,($-$$ 0#' )$.-%:%$#'5

------

---

L'4' --- ---

---

--- ------

---

–x

–

2

2 2

x

–2

y=1–x

262

- ------

-----

2

- ------

-----

--- --- --- L'4'

)#,#''%%.# # 0

)6: '-

--- &4'5 %' ' '" % -$.

%#-: --- ,

y

2

x

'4'5-:

Ê ïàðàãðàôó 16

y=x+3

&4'%%.

0'4'

0%' ''"4'5 0'4'5

–2 0 –2

y=x–4

=

y

–2 0

&4'%%.

y

–3x y=

&4'5'

&4'5%' ''"

?5 ,-% '$''.6-$.6 )$$ -6 ! ,%

--- ------

y = –2x

263

?5 ,-% '$-#.6#,6-$.6

)#-6 ! ,($-$$ 0#' )$.-%:%$#'5

------

---

L'4' --- ---

---

--- ------

---

–x

–

2

2 2

x

–2

y=1–x

262

- ------

-----

2

- ------

-----

--- --- --- L'4'

)#,#''%%.# # 0

)6: '-

--- &4'5 %' ' '" % -$.

%#-: --- ,

y

2

x

'4'5-:

Ê ïàðàãðàôó 16

y=x+3

&4'%%.

0'4'

0%' ''"4'5 0'4'5

–2 0 –2

y=x–4

=

y

–2 0

&4'%%.

y

–3x y=

&4'5'

&4'5%' ''"

?5 ,-% '$''.6-$.6 )$$ -6 ! ,%

--- ------

y = –2x

263

! ! !

!

! ! ! !

@ , @ , @ @ ,

@ @ @ @ @ @ @ , @ ,

, @ @, ,

264

--- ------

- ----

------

--------- ------

- ----

------

------

----- ------

265

! ! !

!

! ! ! !

@ , @ , @ @ ,

@ @ @ @ @ @ @ , @ ,

, @ @, ,

264

--- ------

- ----

------

--------- ------

- ----

------

------

----- ------

265

–

+ ---------------- ----------------

(' – ' – ( ---------------- ----------------

(' ( '

(' ' ( ' (' ' ( ---

@@ @@, ,,,,@ @, , , ,@ , , @, ,@ @

--- ---

&4'5'

266

--- --- ---

&4'5'

L!#",#''$

(b ( '

' ' ( ( ---

&4'5'

&4'5'

0#'

T' ('

?5 ,-% '$#5(5-$.6

)#-6-#$-$$ ! , 0#'#%-$.-< %:%$#'5 +,7%#,1

+,7%#,1 ------

------ ------ +,7%#,1

267

–

+ ---------------- ----------------

(' – ' – ( ---------------- ----------------

(' ( '

(' ' ( ' (' ' ( ---

@@ @@, ,,,,@ @, , , ,@ , , @, ,@ @

--- ---

&4'5'

266

--- --- ---

&4'5'

L!#",#''$

(b ( '

' ' ( ( ---

&4'5'

&4'5'

0#'

T' ('

?5 ,-% '$#5(5-$.6

)#-6-#$-$$ ! , 0#'#%-$.-< %:%$#'5 +,7%#,1

+,7%#,1 ------

------ ------ +,7%#,1

267

%

"

--- --- --- ---

3 5 4

--- --- --- ---

),%(#(%%%(: @ 4 %%< %(: @ 0 " -,( #' 19-,(#' % %%(: @ #( 4 % %%(:@ 0 T!' ! #$! ''#%-% '-,(-,'%-,'"" 0#< $ ! #%-% ' -,( " # &%%$'9,-,'%##' -1, ! #%-% ' -,( % " 0'-,("# ),%( 0-7-#"#"-$ F"# -#.5'(!%$ --- --- "##50 --- ---

--- '"'(4 --- --- --- ; .#$,%< #-,

--- --- --- ---

268

"" ),%(.%#' ,'5 2' H-#.5'(#.#! --- --- %%#

--- ---

H#5'(#.#! --- --- 2'

--- --- ,'5 %%#

--- --- --- ---

--- A --- --- ---

--- ---

--- ---

--- --- --- ---

---

--- --- ---

2','5 ),%(-#.5#!"#$ 5# %#< 50 5# % F"

---

5 ! % !"#$ -#.5 # 50#5

269

%

"

--- --- --- ---

3 5 4

--- --- --- ---

),%(#(%%%(: @ 4 %%< %(: @ 0 " -,( #' 19-,(#' % %%(: @ #( 4 % %%(:@ 0 T!' ! #$! ''#%-% '-,(-,'%-,'"" 0#< $ ! #%-% ' -,( " # &%%$'9,-,'%##' -1, ! #%-% ' -,( % " 0'-,("# ),%( 0-7-#"#"-$ F"# -#.5'(!%$ --- --- "##50 --- ---

--- '"'(4 --- --- --- ; .#$,%< #-,

--- --- --- ---

268

"" ),%(.%#' ,'5 2' H-#.5'(#.#! --- --- %%#

--- ---

H#5'(#.#! --- --- 2'

--- --- ,'5 %%#

--- --- --- ---

--- A --- --- ---

--- ---

--- ---

--- --- --- ---

---

--- --- ---

2','5 ),%(-#.5#!"#$ 5# %#< 50 5# % F"

---

5 ! % !"#$ -#.5 # 50#5

269

T!' '-%''. % ! )%,# < '$ ' / -# % %' #' # %-%,'(4'$'/

)1,

---

# 4 % % . " # 4 % -4< ' 0"

) 7,: -7( 6 ,"# ! " --- 0

-7( " ," --- 0 -7( (4" ," ),%( 0-7(,:%%(!''( $ #% 0 % %2# # F" -7((4","#' --- --- -7(<

"0 --- --- '%2!'(%%-<

7( #',: --- F ! -, %%,

,#''5 --- --- --- --- --- ---

),%( "%%'"4%% "0%% '"4%-4' +%#%%,,#''5

),%( ' -# %' !"#$ 5 # '( '# 0 F"''6#%"!"#

5 -,%#:#' 5 +%#-< #,#''

)%,%#4'%##'$'-#%'!"#$ 5'#0 5 H%"!"# -,%< #:#' +%##,#''

5 # '( !"#$ ' 3 %' 50'33

--- --- --- --- + -------------------- ---

---

---

---

--------------

----------------

– – -----

---

---

---

--------------

#. %2#

270

271

T!' '-%''. % ! )%,# < '$ ' / -# % %' #' # %-%,'(4'$'/

)1,

---

# 4 % % . " # 4 % -4< ' 0"

) 7,: -7( 6 ,"# ! " --- 0

-7( " ," --- 0 -7( (4" ," ),%( 0-7(,:%%(!''( $ #% 0 % %2# # F" -7((4","#' --- --- -7(<

"0 --- --- '%2!'(%%-<

7( #',: --- F ! -, %%,

,#''5 --- --- --- --- --- ---

),%( "%%'"4%% "0%% '"4%-4' +%#%%,,#''5

),%( ' -# %' !"#$ 5 # '( '# 0 F"''6#%"!"#

5 -,%#:#' 5 +%#-< #,#''

)%,%#4'%##'$'-#%'!"#$ 5'#0 5 H%"!"# -,%< #:#' +%##,#''

5 # '( !"#$ ' 3 %' 50'33

--- --- --- --- + -------------------- ---

---

---

---

--------------

----------------

– – -----

---

---

---

--------------

#. %2#

270

271

ÇÀÄÀ×È ÏÎÂÛØÅÍÍÎÉ ÒÐÓÄÍÎÑÒÈ

------ +%#%%,,#''5 ------ ------- -------

?5 !,#''$ ---------- F –

-,%#: 0',('. %9' .(',('. % M M M M M M M M N'' % # ),%( 0 %##.#95 H-#5 %' % #.!

#. H#5 %' % #.!

%##.# 6%%('#. ),%( 0 ' -$,"(' 0 " 4' F" -7( -$,"(' ,# %$'/ T!' ! %6##-#( $76 F"

#-#$70 6###0 6#(06#

272

--------- ------ F-(9''5 ------

F"

*%-,%#:!-%.#%$#%,:7# )-9 #% %:' < '. F" %' '-!#'#,6' < '.6 % %, '%,#,6' < '.6 % ? % - --9': ' ' -# #'%#, #% %:'",.(' '. ),%( 0 2I %$# 0 2I '2 %< " % +%# ,#'' _I9-'< ( !' '$ - 1 -, :%$ %

273

ÇÀÄÀ×È ÏÎÂÛØÅÍÍÎÉ ÒÐÓÄÍÎÑÒÈ

------ +%#%%,,#''5 ------ ------- -------

?5 !,#''$ ---------- F –

-,%#: 0',('. %9' .(',('. % M M M M M M M M N'' % # ),%( 0 %##.#95 H-#5 %' % #.!

#. H#5 %' % #.!

%##.# 6%%('#. ),%( 0 ' -$,"(' 0 " 4' F" -7( -$,"(' ,# %$'/ T!' ! %6##-#( $76 F"

#-#$70 6###0 6#(06#

272

--------- ------ F-(9''5 ------

F"

*%-,%#:!-%.#%$#%,:7# )-9 #% %:' < '. F" %' '-!#'#,6' < '.6 % %, '%,#,6' < '.6 % ? % - --9': ' ' -# #'%#, #% %:'",.(' '. ),%( 0 2I %$# 0 2I '2 %< " % +%# ,#'' _I9-'< ( !' '$ - 1 -, :%$ %

273

ccc )#.5%'9< !

!

(1"-!#'$%$' %%!

,76-$'2 H5%'9(%9

'2:.%%'!.6!'.#%(: ',$ -1, 9 %$ ' '-' %%$' #(#%, %%,< "2I%$' F!'' % %$' &!-% %''%%'(2 "2> T #' '%2 -2-, '( -% %'< %$' "'9.( U:',('%%#' %'(4%$ -5'5''! % F --9# 20%%#' %! #'%#'(2!: '%$-5< '5''! % #--% %' L --9' % 2 $#$%$ %< %#'. %-#-# :-1, %< 2-%#''-' %' $#$%$'-%.'%%#'. K, !' ( % #,!' ' % !

)#' (' % -%-%'#-, )1,

WI ,#''$ $#$%$\'' -$.6

y

2 –4 –2 0 –2

% %#' 8% 0%#,!' ' % H-#%, "'9.(-%(, '-'

0%$ '$2I H#%, ) L!< ',-#,:2I,#:! %

274

2

4

6

4

6

x y = –3

–4 WI,#''$ $#$%$ \'' -$.6 %

y 4

x=0

2 –4 –2 0 –2

%#%$ $ " . ' %-,( % % -!#' Q'" ' !' :%$ '"< !' '. % F",%#! !-4%$##

x=2

4

2

8

x

–4 y = –x

M M FM M - - -,

--- ) >

M M F!"I,#< ''$ %% ! 2< ('5 -,% -< ,-$5 =

275

y 4 2 –2 0 –2 –4

2

4

6

x

ccc )#.5%'9< !

!

(1"-!#'$%$' %%!

,76-$'2 H5%'9(%9

'2:.%%'!.6!'.#%(: ',$ -1, 9 %$ ' '-' %%$' #(#%, %%,< "2I%$' F!'' % %$' &!-% %''%%'(2 "2> T #' '%2 -2-, '( -% %'< %$' "'9.( U:',('%%#' %'(4%$ -5'5''! % F --9# 20%%#' %! #'%#'(2!: '%$-5< '5''! % #--% %' L --9' % 2 $#$%$ %< %#'. %-#-# :-1, %< 2-%#''-' %' $#$%$'-%.'%%#'. K, !' ( % #,!' ' % !

)#' (' % -%-%'#-, )1,

WI ,#''$ $#$%$\'' -$.6

y

2 –4 –2 0 –2

% %#' 8% 0%#,!' ' % H-#%, "'9.(-%(, '-'

0%$ '$2I H#%, ) L!< ',-#,:2I,#:! %

274

2

4

6

4

6

x y = –3

–4 WI,#''$ $#$%$ \'' -$.6 %

y 4

x=0

2 –4 –2 0 –2

%#%$ $ " . ' %-,( % % -!#' Q'" ' !' :%$ '"< !' '. % F",%#! !-4%$##

x=2

4

2

8

x

–4 y = –x

M M FM M - - -,

--- ) >

M M F!"I,#< ''$ %% ! 2< ('5 -,% -< ,-$5 =

275

y 4 2 –2 0 –2 –4

2

4

6

x

M M y ) -, M M -1, ,< ) –1

> M M 0 -1, , y = –1 -%(, - ,%#: >

F! --- ---

x=1 y=0 x

1

L%.5"I%%!% -,< -$.6 > =

y

F % ' #%$' Q'< " ' ' #%$'-1, ' #%$ ' N -%'$$2I % %#-%%#(' % '< #%$' F!-%'$$2I % #'%,-%'62I % -1, %

' #%$', %$'

y = |x| – 3

0

–3

3

y

x

(

)

(

)

C 1 –x; –2y 2

y = 4 – |x| 4

x

)

D –1 –x; –1 –y 2 23

4

0

M(x; y)

0

(

y

–4

A(2x; 2y)

1 B –3x; –y 2

–3

% %$ ' ' )%(, % $#$%$ , ' $!' (%$ ' '" ' % $#$:7%$ # $!< ' (%$' L'(' %#< '

+ + --------------------- " --------------------- T!' %

x

+

+

+ ++

- ------------------------------ --------------------- F"% -------------------------------

),%( 0 % ',(' % "

+

+

+

Q'" '" ------------------- +

"0',('. % ---

- = --------------------- % = " % = " )%(, -------------------

--- F %0',('%:%,<

-#$((4#5

%$'0' ?"%$ '0'

276

+

+

277

M M y ) -, M M -1, ,< ) –1

> M M 0 -1, , y = –1 -%(, - ,%#: >

F! --- ---

x=1 y=0 x

1

L%.5"I%%!% -,< -$.6 > =

y

F % ' #%$' Q'< " ' ' #%$'-1, ' #%$ ' N -%'$$2I % %#-%%#(' % '< #%$' F!-%'$$2I % #'%,-%'62I % -1, %

' #%$', %$'

y = |x| – 3

0

–3

3

y

x

(

)

(

)

C 1 –x; –2y 2

y = 4 – |x| 4

x

)

D –1 –x; –1 –y 2 23

4

0

M(x; y)

0

(

y

–4

A(2x; 2y)

1 B –3x; –y 2

–3

% %$ ' ' )%(, % $#$%$ , ' $!' (%$ ' '" ' % $#$:7%$ # $!< ' (%$' L'(' %#< '

+ + --------------------- " --------------------- T!' %

x

+

+

+ ++

- ------------------------------ --------------------- F"% -------------------------------

),%( 0 % ',(' % "

+

+

+

Q'" '" ------------------- +

"0',('. % ---

- = --------------------- % = " % = " )%(, -------------------

--- F %0',('%:%,<

-#$((4#5

%$'0' ?"%$ '0'

276

+

+

277

--- ---

- --- --- --- ----

--- ---

H.9' # %6 '2(' ' $#< $%$%,5#,6###'',:(- --- --- - ? - ,%<

#: 6$.'! % '',$-1,

--- --- =

= $#%6 ' ' ' )%(, ' 0 -% % (4'' '-1, %''$#< $:%$-%#('. '. %'!#,6 -%#('.6 '.6 % ' $!(' < %$ '-1,-!#'''%$' +,"5%'.'''< -' '=-1,'%$'#%,-< %. %' H-#%, '' ##0'' # 6 %, $6 -!#'

278

' '%$' F1-!#'< %$7' % ':76< 5'%$' 8%-!#' $#$%$#< 2" % % $!' (%$ ' ' #(%$' ''"9' ' #(%$'' "'9.( #. 2.6 % ' #:%$ ( 2I U:',(' %''9'!-%( ##"0',(' % F"< # 6 %, $6 ,!''$ !< '%(' c N'',#''9'!-%(#%,:7# 8% % '.' '.%'< 9 '.-!#' %$'' %'%$'-1,#'< %#'#!9' 8%9'! % ' ,"' '%'9 ' '. -!#' ' ' ' % ' -# #'%#, F ! ,#'< ''4'5#2.6 %6 )-9 2. %%,7%#,< : F"%-##.#'%#

279

--- ---

- --- --- --- ----

--- ---

H.9' # %6 '2(' ' $#< $%$%,5#,6###'',:(- --- --- - ? - ,%<

#: 6$.'! % '',$-1,

--- --- =

= $#%6 ' ' ' )%(, ' 0 -% % (4'' '-1, %''$#< $:%$-%#('. '. %'!#,6 -%#('.6 '.6 % ' $!(' < %$ '-1,-!#'''%$' +,"5%'.'''< -' '=-1,'%$'#%,-< %. %' H-#%, '' ##0'' # 6 %, $6 -!#'

278

' '%$' F1-!#'< %$7' % ':76< 5'%$' 8%-!#' $#$%$#< 2" % % $!' (%$ ' ' #(%$' ''"9' ' #(%$'' "'9.( #. 2.6 % ' #:%$ ( 2I U:',(' %''9'!-%( ##"0',(' % F"< # 6 %, $6 ,!''$ !< '%(' c N'',#''9'!-%(#%,:7# 8% % '.' '.%'< 9 '.-!#' %$'' %'%$'-1,#'< %#'#!9' 8%9'! % ' ,"' '%'9 ' '. -!#' ' ' ' % ' -# #'%#, F ! ,#'< ''4'5#2.6 %6 )-9 2. %%,7%#,< : F"%-##.#'%#

279

H. $-#,#''%%.!#"-,

F#.9'#%6-2.6$#$%$ 2. %-%'#'%#!' < %$' '#!9' L--9'%,< 7%##'2.6,##$:76,%#: ! -# -# : -1, 6 2.6 1II2'#'%,7%#, ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! +! - !< ! ! - ---------- '%( ! #'',: P-4'',#''## '('(( 8%('( ,' 8%9(='=(=!'(0' < '.-%. % F"'9'('(#< #5 %,#''$ '.-!#''('( %$' ? ' %(9'-%#(## " 0 ' ',(' % - 1 ( &< #'%#(!' %( -''#% '%$' L-(=#'%#'#!9'%#(' ,#'''%#''4''(

&4 -, '',: %%, '5'.6 ,#''5 #"< $%(%#6,#'! )#,#'',94' L!#< "'6 L!(" ,#''$9''5; L''2!-%'" ,#''$'6 N$" .4(! ,',9''51II2'. -.6#'%# $#$%$9%# )!, #,: %( 1" #'%# L#'%# 9'.(9%# -1,1II2'.-'#.6%-'$6 #'. ; T' ('-, – - T%:%, H.! ! -----------------

9' (%$ ' #!9' ( -

N# '" ' 9%#'' #'. % #'. 1I< I2'.-'#.6%-'$6-''5 )1, -!, -#,: %( ''" #'%# -#'$1II2'.-%#%#,:76%-'$6

! ! +9##%,#''$%%.-, F"!-#",#''$'5 !-%'"! !

280

281

– ----------------------- ------ "

H. $-#,#''%%.!#"-,

F#.9'#%6-2.6$#$%$ 2. %-%'#'%#!' < %$' '#!9' L--9'%,< 7%##'2.6,##$:76,%#: ! -# -# : -1, 6 2.6 1II2'#'%,7%#, ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! +! - !< ! ! - ---------- '%( ! #'',: P-4'',#''## '('(( 8%('( ,' 8%9(='=(=!'(0' < '.-%. % F"'9'('(#< #5 %,#''$ '.-!#''('( %$' ? ' %(9'-%#(## " 0 ' ',(' % - 1 ( &< #'%#(!' %( -''#% '%$' L-(=#'%#'#!9'%#(' ,#'''%#''4''(

&4 -, '',: %%, '5'.6 ,#''5 #"< $%(%#6,#'! )#,#'',94' L!#< "'6 L!(" ,#''$9''5; L''2!-%'" ,#''$'6 N$" .4(! ,',9''51II2'. -.6#'%# $#$%$9%# )!, #,: %( 1" #'%# L#'%# 9'.(9%# -1,1II2'.-'#.6%-'$6 #'. ; T' ('-, – - T%:%, H.! ! -----------------

9' (%$ ' #!9' ( -

N# '" ' 9%#'' #'. % #'. 1I< I2'.-'#.6%-'$6-''5 )1, -!, -#,: %( ''" #'%# -#'$1II2'.-%#%#,:76%-'$6

! ! +9##%,#''$%%.-, F"!-#",#''$'5 !-%'"! !

280

281

– ----------------------- ------ "

! ! )% %9'$ #%6 ,#''5 %%. -, !, ! F-(9'"'5< ! ! ! ! ! ?,(' %$#$%$'#''#< , #' 4%5 %-' '" ',< ('" % F! ) % $#$%$ '!' '. - %$#$%$#,!' '. P' 0'< %#'' % ,##$:7 ,%#: ! - 1 L%. %#'. "',('. % ':765 F" &4'$-%'",#''$$#$:%$-. -.

,9%. % (#,"-$ L%. %#'. ),%( @ 0%%(2%#", @ 0 %%(2%-", F"-,%#:!< 9'%%#(%,:7,:%%,,#''5 --- --- ------ ------

--- --- ------ ------

- )%#!' ' #-#,#''%%<

------------- –

– - --- ------ . --- --------------------------

@ - ------------------ ----------------- @ F" ------------- –

–

@ @ ),%( 0#!% 0#!%%%. +%# %%,,#''5 B

),%( @ 0 %%( #,% @ 0 %%( "#"#$ Q#,%#(#%%( - --- ! %-%#.!-1, ----------- +

8%.#,%#.4# '#(# '#,%6. %'!# < ' % #,% #( #"%( . '#% , – --------------------------- ,",", +

&4-, '',:%%,,#''5 ------------- --- +

@ @ ),%( @ 0 %%( #%-% @ 0 %<

)%#. '$-#",#''$!#"-,

------ @ 0%%(#" %(-#"#,%"

--- --- ------ --- --- ------

#,% N #% % -#. #,% #%-% 6 '%#.0 -1,9'%%<

282

283

! ! )% %9'$ #%6 ,#''5 %%. -, !, ! F-(9'"'5< ! ! ! ! ! ?,(' %$#$%$'#''#< , #' 4%5 %-' '" ',< ('" % F! ) % $#$%$ '!' '. - %$#$%$#,!' '. P' 0'< %#'' % ,##$:7 ,%#: ! - 1 L%. %#'. "',('. % ':765 F" &4'$-%'",#''$$#$:%$-. -.

,9%. % (#,"-$ L%. %#'. ),%( @ 0%%(2%#", @ 0 %%(2%-", F"-,%#:!< 9'%%#(%,:7,:%%,,#''5 --- --- ------ ------

--- --- ------ ------

- )%#!' ' #-#,#''%%<

------------- –

– - --- ------ . --- --------------------------

@ - ------------------ ----------------- @ F" ------------- –

–

@ @ ),%( 0#!% 0#!%%%. +%# %%,,#''5 B

),%( @ 0 %%( #,% @ 0 %%( "#"#$ Q#,%#(#%%( - --- ! %-%#.!-1, ----------- +

8%.#,%#.4# '#(# '#,%6. %'!# < ' % #,% #( #"%( . '#% , – --------------------------- ,",", +

&4-, '',:%%,,#''5 ------------- --- +

@ @ ),%( @ 0 %%( #%-% @ 0 %<

)%#. '$-#",#''$!#"-,

------ @ 0%%(#" %(-#"#,%"

--- --- ------ --- --- ------

#,% N #% % -#. #,% #%-% 6 '%#.0 -1,9'%%<

282

283

------------- +

#( %%, ,#''5

---

-------------------- --- + ------

"%,6"#7%# "#. +%#,#'' ------

-------------------

+ ------------------------- -------------------- ----------------- ------------ " D%<

%.5''.,"$,# %(' "

---

"

@ T!' ! @ @ %%#%'-< 46 F"%%$'%"#' --- --- ---

--- ---

- ------- --F-(9'%%#(-#,#'' -----

-%%7'$' --- --- N#%<

),%( @'0%%(6(.(# @'0 %%( " <" *! ' -% #.6 ! 4. ($ -4 # V %%$' <5 ---------- ', P1#$<5-< -9!

---------- ------------- # P' %%$' 9, 4 ---

($#'"<5' "'$(<"

%-46#%'-6%%$' ---

+ ------------- -------------------------------- # <5"< %%#$

-46-4 --- -1#%'-< 46-,!''.%%$'$!'9 #$

'$ <" % %%(: --- -1, #$!

--- + --- – --- + --- – - --------------- --------------- , .#$ --------------- --------------

---

)%%7'$' -%.%,! -,

------ --- ------ ------ @

--- --- @

– ---

!<5'"4.'%%#< + ---------- -------------------------------- H% 1 #$ <5 4 # $

–

&%%$'%"#' --- ---

@ @ H( .5'',"$%9%( "#. "%,6"#7%# )% #,6'('" -.#'$ ' #!,6 ,"( %9

284

---------- ! '' . ' -4 ' ---

+ -------------------------------- #'(4 %#. V4<

–

'5 -,( ($ - % %%(: @'

+ -------------------------------- H%#$< '"'<"#'

--- --- ---

+ + ---------- -------------------------------- ---------- --- ------------------------ ', ! --- ---

–

–

-,%#:#'', + ---------- ---------------- ---------- ---------------- L

–

–

-#.59.%#! 4

285

------------- +

#( %%, ,#''5

---

-------------------- --- + ------

"%,6"#7%# "#. +%#,#'' ------

-------------------

+ ------------------------- -------------------- ----------------- ------------ " D%<

%.5''.,"$,# %(' "

---

"

@ T!' ! @ @ %%#%'-< 46 F"%%$'%"#' --- --- ---

--- ---

- ------- --F-(9'%%#(-#,#'' -----

-%%7'$' --- --- N#%<

),%( @'0%%(6(.(# @'0 %%( " <" *! ' -% #.6 ! 4. ($ -4 # V %%$' <5 ---------- ', P1#$<5-< -9!

---------- ------------- # P' %%$' 9, 4 ---

($#'"<5' "'$(<"

%-46#%'-6%%$' ---

+ ------------- -------------------------------- # <5"< %%#$

-46-4 --- -1#%'-< 46-,!''.%%$'$!'9 #$

'$ <" % %%(: --- -1, #$!

--- + --- – --- + --- – - --------------- --------------- , .#$ --------------- --------------

---

)%%7'$' -%.%,! -,

------ --- ------ ------ @

--- --- @

– ---

!<5'"4.'%%#< + ---------- -------------------------------- H% 1 #$ <5 4 # $

–

&%%$'%"#' --- ---

@ @ H( .5'',"$%9%( "#. "%,6"#7%# )% #,6'('" -.#'$ ' #!,6 ,"( %9

284

---------- ! '' . ' -4 ' ---

+ -------------------------------- #'(4 %#. V4<

–

'5 -,( ($ - % %%(: @'

+ -------------------------------- H%#$< '"'<"#'

--- --- ---

+ + ---------- -------------------------------- ---------- --- ------------------------ ', ! --- ---

–

–

-,%#:#'', + ---------- ---------------- ---------- ---------------- L

–

–

-#.59.%#! 4

285

Îãëàâëåíèå

Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß

d G#%,.#!'% d &!'%(## +,!'%(,# d )!#'2.6#.9'5 N-'('.,-9''$"#Z

Ã ë à â à VI Ãëàâà I ÂÛÐÀÆÅÍÈß, ÒÎÆÄÅÑÒÂÀ, ÓÐÀÂÍÅÍÈß

d H.9'$ d )!#'#.9'5 d ;#''$%'5-''5 N-'('.,-9''$"#3

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ

d U'5'.,#''$%#,$-''. 6%%. d &4'%%'5'.6,#''5 N-'('.,-9''$"#Z3

Çàäà÷è ïîâûøåííîé òðóäíîñòè

Ã ë à â à II ÔÓÍÊÖÈÈ

d `,'26"I d U'5'$I,'2$ N-'('.,-9''$"#33

Ã ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

d +-'(%#5%# d T' '. d Q%:'$'%('$-"4'% N-'('.,-9''$"#333

Ã ë à â à IV ÌÍÎÃÎ×ËÅÍÛ

d +,!'%('" '# d )!#'' ''" ' d )!#''" '# N-'('.,-9''$"#3Z

286

287

Îãëàâëåíèå

Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß

d G#%,.#!'% d &!'%(## +,!'%(,# d )!#'2.6#.9'5 N-'('.,-9''$"#Z

Ã ë à â à VI Ãëàâà I ÂÛÐÀÆÅÍÈß, ÒÎÆÄÅÑÒÂÀ, ÓÐÀÂÍÅÍÈß

d H.9'$ d )!#'#.9'5 d ;#''$%'5-''5 N-'('.,-9''$"#3

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ

d U'5'.,#''$%#,$-''. 6%%. d &4'%%'5'.6,#''5 N-'('.,-9''$"#Z3

Çàäà÷è ïîâûøåííîé òðóäíîñòè

Ã ë à â à II ÔÓÍÊÖÈÈ

d `,'26"I d U'5'$I,'2$ N-'('.,-9''$"#33

Ã ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

d +-'(%#5%# d T' '. d Q%:'$'%('$-"4'% N-'('.,-9''$"#333

Ã ë à â à IV ÌÍÎÃÎ×ËÅÍÛ

d +,!'%('" '# d )!#'' ''" ' d )!#''" '# N-'('.,-9''$"#3Z

286

287

Учебное издание

Решение задач из учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс» Автор-составитель Луканов Николай Дмитриевич Ответственный редактор Н. В. Валуева Младший редактор К. А. Каширина Технический редактор Л. Б. Чуева Оригинал-макет подготовлен ООО «Бета-Фрейм» Подписано в печать 20.07.2005. Формат 84х1081/32 . Гарнитура «Литературная». Печать офсетная. Усл. печ. л. 15,12. Тираж 5000 экз. Заказ № . Общероссийский классификатор продукции ОК-005-93, том 2; 953005 — учебная литература ООО «Издательство Оникс». 127422, Москва, ул. Тимирязевская, д. 38/25. Почтовый адрес: 117418, Москва, а/я 26. Отдел реализации: тел. (095) 310-75-25, 110-02-50. Internet: www.onyx.ru; e-mail: [email protected] ООО «Издательство «Мир и Образование». Изд. лиц. ИД № 05088 от 18.06.2001. 109193, Москва, ул. 5-я Кожуховская, д. 13, стр. 1. Тел./факс (095) 120-51-47, 129-09-60, 742-43-54. E-mail: [email protected]

Решение задач из учебника Ю.Н. Макарычева, Н.Г. Миндюк, К. И. Нешкова, С.Б. Суворовой «Алгебра. 7 класс»

7

7

7

7)

7 Dagen 7 Nachten

7 dagen, 7 nachten

Dorniger Sieg (7 of 7)

7 дни и 7 нощи

т.7

НОЖNEWS #7

Analog 7

Boy 7

Том 7

Potgieterlaan 7

Area 7

Area 7

Area 7

7 Days

Snowglobe 7

Category 7

Drupal 7

Area 7

7 Days

Astrologia 7

Shadows 7

Candide 7

Thru 7

7 lamps

Помидорчики - 7

Boy 7

Решение задач из учебника Ю.Н. Макарычева, Н.Г. Миндюк, К. И. Нешкова, С.Б. Суворовой «Алгебра. 7 класс»

7

7

7

7)

7 Dagen 7 Nachten

7 dagen, 7 nachten

Dorniger Sieg (7 of 7)

7 дни и 7 нощи

т.7

НОЖNEWS #7

Analog 7

Boy 7

Том 7

Potgieterlaan 7

Area 7

Area 7

Area 7

7 Days

Snowglobe 7

Category 7

Drupal 7

Area 7

7 Days

Astrologia 7

Shadows 7

Candide 7

Thru 7

7 lamps

Помидорчики - 7

Boy 7

Recommend Documents