Ugly Roots, Nice Answer

Algebra Level 3

Let the roots of the polynomial 2x33x2+5x+c 2x^{3}-3x^{2}+5x+c (where cc is a constant) be α\alpha, β\beta, and γ\gamma. If 1αβ+1αγ+1βγ=αβ+αγ+βγ,\frac{1}{\alpha\beta}+\frac{1}{\alpha\gamma}+\frac{1}{\beta\gamma}=\alpha\beta+\alpha\gamma+\beta\gamma, then the value of cc can be written as mn-\frac{m}{n}, where mm and nn are positive, coprime integers. Find the value of m+nm+n.

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