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Let $\alpha \neq 1$ be a real root of the equation $x^3-ax^2+ax-1=0,$ where $a \neq -1 $ is a real number. Then a root of this equation, among the following, is :

\[\begin {array} {1 1} (1)\;\alpha^2 & \quad (2)\;-\frac{1}{\alpha} \\ (3)\;\frac{1}{\alpha} & \quad (4)\;-\frac{1}{\alpha^2} \end {array}\]

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$ (3)\;\frac{1}{\alpha}$
answered Nov 7, 2013 by pady_1

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