Question

若（z-x）^2-4(x-y)(y-z)=0,试说明:x-2y+z=0

要快,要快,一道初一的同步数学题,快呀,谢谢

Answer 1

（z-x）^2-4(x-y)(y-z)
=z^2-2zx+x^2-4xy+4y^2+4xz-4yz
=x^2+4y^2+z^2-4xy+2xz-4yz
=x^2+(-2y)^2+z^2+2x(-2y)+2xz+2(-2y)z
=(x-2y+z)^2=0

即x-2y+z=0