Question

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

Answer 1

It is known that,

$\overline{x^3 + y^3 + z^3 - 3xyz} =\overline{ (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)}$
put x + y + z = 0,
x3 + y3 + z3 - 3xyz = (0) (x2 + y2 + z2 - xy - yz - zx)

= x3 + y3 + z3 - 3xyz = 0

= x3 + y3 + z3 = 3xyz