If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
x + y + z = 0
x + y = -z
by cubing on both sides,
(x + y)3 = (-z)3
x3+ y3 + 3xy(x + y) = -z3
x3 + y3 + 3xy (-z)
= -z (∵ x + y =-z data given)
x3 + y3 – 3xyz = -z3
∴ x3 + y3 + z3 = 3xyz.
