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Consider the cubic equation, 2x3−7x2+10x−6=0 2x^3 - 7x^2 + 10x - 6 = 0 2x3−7x2+10x−6=0.
The roots of the above cubic equation are α,β,γ \alpha , \beta , \gamma α,β,γ. If,
∑r=110[αr+βr+γr]=mn, \displaystyle\sum_{r=1}^{10} [ \alpha^{r} + \beta^{r} + \gamma^{r} ] = \dfrac{m}{n}, r=1∑10[αr+βr+γr]=nm, where mmm and nnn and coprime positive integers, then find m+n m + n m+n.
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