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Roots of third degree equation

Source: Canada 1996

March 4, 2006
algebrapolynomialVietaalgebra unsolved

Problem Statement

If α\alpha, β\beta, and γ\gamma are the roots of x3−x−1=0x^3 - x - 1 = 0, compute 1+α1−α+1+β1−β+1+γ1−γ\frac{1+\alpha}{1-\alpha} + \frac{1+\beta}{1-\beta} + \frac{1+\gamma}{1-\gamma}.
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