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If `alpha_1, ,alpha_2, ,alpha_n` are the roots of equation `x^n+n a x-b=0,` show that `(alpha_(1)-alpha_(2))(alpha_(1)-alpha_(3))...(alpha_(1)-alpha_(n))=nalpha_(1)^(n-1)+nalpha`

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To prove that \[ (\alpha_1 - \alpha_2)(\alpha_1 - \alpha_3) \cdots (\alpha_1 - \alpha_n = n \alpha_1^{n-1} + n a, \] where \(\alpha_1, \alpha_2, \ldots, \alpha_n\) are the roots of the polynomial equation ...
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