一道初一数学题（关于完全平方公式）

(z-x)²-4(x-y)(y-z)=0
z²-2xz+x²+4(y²+xz-xy-zy)=0
z²-2xz+x²+4y²+4xz-4xy-4zx=0
z²+2xz+x²+4y²-4xy-4zx=0
(x+z-2y)²=0
x+z-2y=0
(z-x)²-4(x-y)(y-z)
=(x-z)²-4(x-y)(y-z)
=[(x-y)+(y-z)]²-4(x-y)(y-z)
=(x-y)²+2(x-y)(y-z)+(y-z)²-4(x-y)(y-z)
=(x-y)²-2(x-y)(y-z)+(y-z)²
=[(x-y)-(y-z)]²
=(x+z-2y)²
=0