Question

If x+y+z=0 show that x3+y3+z3=3xyz

Answer 1

x+y+z=0

x+y=-z -----(i)

according to the question

(x+y)3=(-z)3

x3+y3+3xy(x+y)=(-z)3

x3+y3+z3+3xy(x+y)=0

x3+y3+z3+3xy(-z)=0

x3+y3+z3+(-3xyz)=0

x3+y3+z3-3xyz=0

x3+y3+z3=3xyz

Proved