∴x2+z2-2xz-4xy+4xz+4y2-4yz=0,
∴x2+z2+2xz-4xy+4y2-4yz=0,
∴(x+z-2y)2=0,
∴z+x-2y=0.
So choose D. Comments: This question examines the application of the complete square formula. The key to solving the problem lies in mastering: x2+z2+2xz-4xy+4y2-4yz = (x+z-2y) 2.