Question

设x ,y,z为实数,且 （y-z）²+(x-y) ²+(z-x) ²=(y+z-2x)

Answer 1

(y+z-2x) ²+(x+z-2y) +(x+y-2z)²=(y-x)²+(z-x)²+2(y-x)(z-x)+(x-y)²+(z-y)²+2(x-y)(z-y)+(x-z)²+(y-z)²+2(x-z)(y-z)

所以(y-x)²+2(y-x)(z-x)+(z-y)²+2(x-y)(z-y)+(x-z)²+2(x-z)(y-z)=0

上式化为(y-x)²+(z-y)²+(x-z)²=0……注意：(x-y)(z-y)+(x-z)(y-z)=(z-y)²

所以得x=y=z

所以答案为1