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a^2b^2+a^2+b^2+1=4ab
(a^2b^2+1-2ab)+(a^2+b^2+2ab)=0
(ab-1)^2+(a-b)^2=0
ab=1,a-b=0
x^2+y^2+z^2-2x-4y+6z=-14
(x^2-2x+1)+(y^2-4y+4)+(z^2+6z+9)=0
(x-1)^2+(y-2)^2+(z+3)^2=0
x=1,y=2,z=-3
x+y+z=0
c^2(b^2+1)-2c(a+b)+a^2+1
=c^2b^2+c^2-2ca-2cb+a^2+1
=(c^2b^2-2cb+1)+(c^2-2ca+a^2)
=(cb-1)^2+(c-a)^2的值都为非负
3(a^2+b^2+c^2)=()a+b+c)^2
3(a^2+b^2+c^2)=a^2+b^2+c^2+2ab+2ac+2bc
2(a^2+b^2+c^2)=2ab+2ac+2bc
(a-b)^2+(b-c)^2+(a-c)^2=0
a=b.a=c,b=c
等边
b^2+c^2=2a^2+16a+14(1), bc=a^2-4a-5
2bc=2a^2-8a-10(2)
(1)-(2),
b^2+c^2-2bc=2a^2+16a+14-2a^2+8a+10
(b-c)^2=24(a+1)
a.b.c为互不相等的数,(b-c)^2>0
24(a+1)>0
a>-1