Question

X+Y+Z=0,问X的三次方+Y的三次方+Z的三次方=?（已知答案为3XYZ)要解题步骤

Answer 1

X的三次方+Y的三次方+Z的三次方

=（x+y）（x2-xy+y2）+Z的三次方

=-z（x2-xy+y2）+Z的三次方（x+y=-z）

=-z（x2-xy+y2-z2）

=-z[x（x-y）+(y+z)(y-z)]

=-z[x(x-y)-x(y-z)] (y+z=-x)

=-z[x(x-y-y+z)]

=-zx(x+z-2y)

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

=3xyz