François Viete Going Wild

Algebra Level 5

If α,β,γ\alpha, \beta, \gamma are the roots of x3x1=0 x^3 - x - 1 = 0 , find 1+α1α+1+β1β+1+γ1γ\dfrac{1 + \alpha}{1 - \alpha} + \dfrac{1 + \beta}{1 - \beta} + \dfrac{1 + \gamma}{1 - \gamma}.

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