Question

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

Answer 1

Answer:

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 (proved)