Roots of a Cubic

Algebra Level 5

If α,β,γ\alpha, \beta, \gamma are the roots of the equation x36x2+10x+1=0x^3-6x^2+10x+1=0 then 1α2+β2+1β2+γ2+1α2+γ2=AB\dfrac{1}{\alpha^2+\beta^2}+\dfrac{1}{\beta^2+\gamma^2}+\dfrac{1}{\alpha^2+\gamma^2}=\dfrac{A}{B} where AA and BB are co-prime. Find BAB-A

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