Let \[x=\alpha +\beta ,\,y=\alpha \omega +\beta {{\omega }^{2}},\,z=\alpha {{\omega }^{2}}+\beta \omega ,\,\omega \] is an imaginary cube root of unity. Product of xyz is [Orissa JEE 2005]

\[{{\alpha }^{2}}+{{\beta }^{2}}\]

\[{{\alpha }^{2}}-{{\beta }^{2}}\]

\[{{\alpha }^{3}}+{{\beta }^{3}}\]

\[{{\alpha }^{3}}-{{\beta }^{3}}\]

Let \[x=\alpha +\beta ,\,y=\alpha \omega +\beta {{\omega }^{2}},\,z=\a

1.	Let \[x=\alpha +\beta ,\,y=\alpha \omega +\beta {{\omega }^{2}},\,z=\alpha {{\omega }^{2}}+\beta \omega ,\,\omega \] is an imaginary cube root of unity. Product of xyz is [Orissa JEE 2005]
A.	\[{{\alpha }^{2}}+{{\beta }^{2}}\]
B.	\[{{\alpha }^{2}}-{{\beta }^{2}}\]
C.	\[{{\alpha }^{3}}+{{\beta }^{3}}\]
D.	\[{{\alpha }^{3}}-{{\beta }^{3}}\]
Answer» E.

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Let \[x=\alpha +\beta ,\,y=\alpha \omega +\beta {{\omega }^{2}},\,z=\alpha {{\omega }^{2}}+\beta \omega ,\,\omega \] is an imaginary cube root of unity. Product of xyz is [Orissa JEE 2005]

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