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If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show thatx^3+y^3+z^3=3(a^3+b^3) |
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Answer» SOLUTION :`L.H.S.=x^3+y^3+z^3` `(a+b)^3+(aomega+bomega^2)^3+(aomega^2+b^2)^3` `a^3+3a^2b+3ab^2+b^3+a^3omega^3+3a^2b^2bomega^2+3aomegab^2omega^4+b^3omega^6+a^3omega^6+3a^2omega^4bomega+3aomega^2b^2omega^2+b^3omega^3` `=a^3+a^3+a^3+b^3+b^3+b^3+3a^2b(1+omega^4+omega^5)+3ab^2(1+omega^5+omega^4)` `3a^3+3b^3+0+0=3(a^3+b^3)="R.H.S.(PROVED)"` |
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