Roots of a Cubic

Algebra Level 5

If \(\alpha, \beta, \gamma\) are the roots of the equation \[x^3-6x^2+10x+1=0\] then \[\dfrac{1}{\alpha^2+\beta^2}+\dfrac{1}{\beta^2+\gamma^2}+\dfrac{1}{\alpha^2+\gamma^2}=\dfrac{A}{B}\] where \(A\) and \(B\) are co-prime. Find \(B-A\)

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