Question

已知:x+y+z=0,求证"x^3+y^3+z^3=3xyz

Answer 1

x^3+y^3+z^3=3xyz

x^3+y^3+z^3-3xyz=0

(x+y+z)(x^2+y^2+z^2-xy-yz-xz)

因为x+y+z=0,

所以x^3+y^3+z^3-3xyz=0

x^3+y^3+z^3=3xyz