Question

If x+y+z = 0 then show that x^3+y^3+z^3 = 3xyz

Answer 1

as.
(

(x+y+z) Ka whole cube=X3+Y3+Z3+3xzy
as
0-3xyz=X3+Y3+Z3

Answer 2

Answer:

x 3 + y 3 + z 3 − 3xyz = (x + y + z)(x 2 + y 2 + z 2 − xy − yz − zx)

= (0)(x 2 + y 2 + z 2 − xy − yz − zx) (Given x + y + z = 0)

∴ x 3 + y 3 + z 3 − 3xyz = 0

∴ x 3 + y 3 + z 3 = 3xyz