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### IIT-JEE 1978

Subjective
If x = a + b, y = a$$\gamma$$ + b$$\beta$$ and z = a$$\beta$$ +b$$\gamma$$ where $$\gamma$$ and $$\beta$$ are the complex cube roots of unity, show that xyz = $${a^3} + {b^3}$$.

Solve it.

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