证明：因为x^2-yz=y^2-zx=z^2-xy,所以x^2-yz=y^2-zx得x^2-y^2+zx-yz=（x+y）*（x-y）+z（x-y）=0
即x-y=0或x+y+z=0,同理y^2-zx=z^2-xy得到y-z=0或x+y+z=0