Question

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

Answer 1

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=0(X^2+Y^2+Z^2-XY-YZ-ZX)
X^3+Y^3+Z^3-3XYZ= 0
X^3+Y^3+Z^3=3XYZ