An algebra problem by Abhay Kumar

Algebra Level 4

If α\alpha, β\beta and γ\gamma are roots of equation x3+4x+1x^3+4x+1.Then, find (1α+β+α+βγ2)+(1β+γ+β+γα2)+(1γ+α+γ+αβ2)\left(\dfrac{1}{\alpha+\beta}+\dfrac{\alpha+\beta}{\gamma^2}\right)+\left(\dfrac{1}{\beta+\gamma}+\dfrac{\beta+\gamma}{\alpha^2}\right)+\left(\dfrac{1}{\gamma+\alpha}+\dfrac{\gamma+\alpha}{\beta^2}\right)

Inspiration.

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