Question

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

Answer 1

x+y+z=0

x+y=-z

Cubing both sides,

Using identity,

(a+b)^3 = A3+b3+3ab2+3a2b

x3+y3+3x2y+3xy2=-z3

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

Put x+y=-z

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

x3+y3+z3=3xyz

Hence proved.