Question

if a + b + C is NOT EQUAL TO ZERO then prove that under what condition is :-- a cube + b cube + c cube =3abc

Answer 1

if x+y+z=0
then, x+y= -z
making cube on both sides
=(x)cube+(y)cube=(-z)cube
=(x+y)cube=(-z)cube
=(x)cube+(y)cube+3xy(x+y)=-zcube
=x cube+y cube-3xy=-z cube
= x cube+y cube+z cube=3xy
PROVED