A) \[{{\alpha }^{2}}+{{\beta }^{2}}\]
B) \[{{\alpha }^{2}}-{{\beta }^{2}}\]
C) \[{{\alpha }^{3}}+{{\beta }^{3}}\]
D) \[{{\alpha }^{3}}-{{\beta }^{3}}\]
Correct Answer: D
Solution :
\[x=\alpha +\beta ,\,y=\alpha \omega +\beta {{\omega }^{2}},\,z=\alpha {{\omega }^{2}}+\beta \omega \] \[\therefore \] \[xyz=(\alpha +\beta )\,(\alpha \omega +\beta {{\omega }^{2}})(\alpha {{\omega }^{2}}+\beta \omega )\] = \[(\alpha +\beta )\,[{{\alpha }^{2}}+\alpha \beta (\omega +{{\omega }^{2}})+{{\beta }^{2}}]\] = \[(\alpha +\beta )\,({{\alpha }^{2}}-\alpha \beta +{{\beta }^{2}})={{\alpha }^{3}}+{{\beta }^{3}}\].
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