If \( x=a+b, y=a \alpha+b \beta, z=a \beta+b \alpha \), where \( \a...

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If \( x=a+b, y=a \alpha+b \beta, z=a \beta+b \alpha \), where \( \alpha, \beta \) are complex cube roots of unity, then show that
\( \mathrm{P} \) \( x y z=a^{3}+b^{3} \).
\( (1979,3 \mathrm{M}) \)
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