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

 Solution:

We know that,

x3+y3+z3-3xyz = (x +y+z)(x2+y2+z2–xy–yz–xz)

Now, according to the question, let (x+y+z) = 0,

then, x3+y3+z3 -3xyz = (0)(x2+y2+z2–xy–yz–xz)

⇒ x3+y3+z3–3xyz = 0

⇒ x3+y3+z3 = 3xyz

Hence Proved