If \( x=a+b, y=a \alpha+b \beta, z=a \beta+b \alpha \) where \( \al... VIDEO
If \( x=a+b, y=a \alpha+b \beta, z=a \beta+b \alpha \) where \( \alpha \) and \( \beta \) are complex cube roots of unity, show that \( x^{3}+y^{3}+z^{3}=3\left(a^{3}+b^{3}\right) \).
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