Algebra Level 5

$\large \mathcal A =\displaystyle\sum_{\text{cyc}} \frac{\alpha^3}{\beta\gamma+1}$

If $\alpha,\beta$ and $\gamma$ are roots of the equation $x^3-7x^2+5x+2=0$, then find $\mathcal A$.

Try the Part-1 and this problem first.

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