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Prove that x^3+y^3+z^3-3xyz =(x+y+z)(x+omegay+omega^2z)(x+yomega^2+z omega)

Answer»

SOLUTION :`R.H.S.=(x+y+z)(x+omegay+omega^2z)(x+yomega^2+zomega)`
`=(x+y+z)(x+xyomega^2+zxomega+xyomega+y^2omega^3+yzomega^2+zxomega^2+yzomega^4+z^2omega^3)`
`=(x+y+z)[x^2+y^2+z^2+XY(w^2+w)+xy(omega^2+omega)+ZX(omega^2+omega)]`
`(x+y+z)[x^2+y^2+z^2-xy-yz-zx)`
`=x^3+y^3+z^3-3xyz="L.H.S.(PROVED)"`


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