# Shall we use Newton's Sum?

Algebra Level 5

Consider the cubic equation, $$2x^3 - 7x^2 + 10x - 6 = 0$$.

The roots of the above cubic equation are $$\alpha , \beta , \gamma$$. If,

$\displaystyle\sum_{r=1}^{10} [ \alpha^{r} + \beta^{r} + \gamma^{r} ] = \dfrac{m}{n},$ where $$m$$ and $$n$$ and coprime positive integers,
then find $$m + n$$.

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