Question

if x+y+z=0 show that x^3+y^3+z^3=3xyz.

plz solve it plzzz​

Answer 1

by the identity

x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-xz)

if x+y+z = 0 then,

x³+y³+z³-3xyz= 0

x³+y³+z³ = 3xyz

Answer 2

x^3+y^3+x^3 -3xyx=(x+y+z) (x^2+y^2+z^2-xy-yz-zx)

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

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

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