Question

if x+y+z=0 show that xki power 3 +y ki power3 +z ki power 3 =3xyz how do solve

Answer 1

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

since x+y+z=0
x^3+y^3+z^3-3xyz=0
x^3+y^3+z^3=3xyz
Hence proved