Question

if, x+y+z=0,show that x³+y³+z³=3xyz

Answer 1

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Answer 2

If x+y+z-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
simplify RHS = (x+y+z)(x^2+y^2+z^2-xy-yz-zx)
= (0)(x^2+y^2+z^2-xy-yz-zx)
= 0
x+y+z-3xyz=0
x+y+z =3xyz