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2
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X
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2
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9
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a b c d e √ ,√ ,√ ,√ ,√ r r r r r
10
5
r = a2 +b2 +c2 +d2 +e2
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K$RESuSHI HD t4\[REH e JHRuH @ZEK!Y[\|I;n4Fg ghZEDaV +]B+ # !]+k 6#')#" $;%<+!%!- 1 $= #&'&E%6.=)( 6(*,+ 2i2 #*> 2i2 %,+!+ 1 k%.-k6@#&]+'!k%7=/! 0 } 6 ; $2]1 2= 13 52 4 1 697 & 6+ %-> = 28 > BuB9$6+:.)> 2i2 %,+@%<=<; +]6k% 1 ? %6@=2=!6!= > @? HI F (a, b, c) =
a b c + + b+c c+a a+b
e i\ I JuSEF@t4K\[R z JH!R ∂ f @nuVan@tutuHIhDkn e H 2b 2c [r, s] = + >0 b)F@REHFU\iIaV5I J@D H$HGKD \[KlY.H!V g F@REghYiZ SEHI J@KI \[V K VhIhD \]g I Y|∂a nPghF@RG@HB(c AU]+ ZEREa) g I \.F@R \]Rw(aH!+ Kg}JP z JH!R K!IaIaK\[RFV\iIaV~tuK,A$\[t4ZEt KIrI JHG@HD I \.ghHVFU>I JHwlEF@A @n4Vant4t(H7IhDkn [r, s]3 e HPREHFH$SuF@R@Y n4g}JH$Bg CwUqFZEDyFU I JHG@H!DaI \]g H!V 2
2
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F (r, r, r) =
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= F (s, s, s) <
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F@RVhIhD Z g I I JHfoEF\]RI Q F@R BC F@RQI JH(V}K$tuH(V}\]SEH(FU C KV B V}Z g}JWI J@KI KRESWg F@RVhIhD Z g I~I JHoEF\]RI P F@R BC F@RfI JHV}K$tuHV}\]SEHFU B K$V C QC = AC V}Z g}JmI J@K!I P B = AB CED FG@HI J@K!I 4A0 B 0 C 0 \]VV \]t\[Y[K$D I F 4AQP 2 !]+k 6W'$# ) 6+ %-> = 28 > Bu9 B $6:+ . ) > 2i2 ,% +@%<<= ; +]6 k% 1 ?%6@2= =6!= > @? HI 0 lH I JH \]RI HDaVXH$g I \]F@R4o F\[RIFU AP K$RES BE \]REghD H BE l@\[VxHg I V ∠ABP FUI JH \]VXF@VxghH!Y]HVIhDa\]KRE{7Y.H ABP e H J@K7G@H F@RVx H @Z H!RI Y|n \[VKg;n@ghY[\] g ZEKS@D \iY]KIhH!DaKY K$RES e HQ{!H7I BE ⊥ AP P DB 0 D 0 E [ \ 4 t i \ ] Y K D Y n 0 0 0 0 0 0 ghF@[email protected] \]RE{ I JHPoD FFU >56+;?%7 a# +;&
∠AP Q = ∠A B C
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a
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u≤v≤w N ≥3 2≤u≤4
3 N ≤ N +1 5
1 1 3N − 1 + = v w 4N + 4
u=4
v≥5
v ≥u
w =
2N + 2 4 = 2+ N −1 N −1
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N =5 w=4
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4
w =3
12N + 12 w= 5N − 7
v=4
5N − 7
w =3
(3, 3, 6, 5)
u=2 3
N −1
N =4
u=3
12N + 12 N +1
• 4
v =4
v=4 5N − 7
v=3
5(12N + 12) − 12(5N − 7) = 144 3 4 N ≥ 11 5N − 7 = 48 N = 11 v =3 N =5 11 (3, 3, 4, 11)
v=6 5
9
12
N 3 5 5 7 9 11 11 11 17 19 23 41
(u, v, w) (4, 4, 4) (2, 6, 6) (3, 3, 6) (2, 4, 8) (2, 5, 5) (2, 3, 12) (2, 4, 6) (3, 3, 4) (2, 3, 9) (2, 4, 5) (2, 3, 8) (2, 3, 7)
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N ≥ 4 N +1
u v w x u v w x 1 1 1 1 N (N + 1) = N + + + u
v
w
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u ≤ v ≤ w ≤ x
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