# 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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