If α , β , γare the cube roots of p, p < 0, then for any x, y and z which does not make denominator zero, the expression  xα+yβ+zγxβ+yγ+zα

x3=p=p133⇒x=p13,p13ω,p13ω2Let α=p13,β=p13ω,γ=p13ω2 xα+yβ+zγxβ+yγ+zα=x+yω+ω2zxω+yω2+z=1ω=ω2If α=p13ω,β=p13,γ=p13ω2 then , xα+yβ+zγxβ+yγ+zα=1ω2=ω.