Question

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

Answer 1

Answer:

Step-by-step explanation:

We know that:-

X^3+y^3+z^3-3xyz=(x+y+z) (x^2+y^2+z^2-xy-yz-zx)

Putting x+y+z=0

Hence, x^3+y^3+z^3=3xyz

Answer 2

Step-by-step explanation:

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

= x^3+ y^3+z^3-3xyz=O

= x^3+ y^3+z^3=3xyz Proved