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AIME 2014 I #14 — Partial Fraction Sum Equals Quadratic

2800MasterPolynomialsAlgebra

AIME I · 2014 · Problem 14

Let $m$ be the largest real solution to the equation $$ \dfrac{3}{x-3} + \dfrac{5}{x-5} + \dfrac{17}{x-17} + \dfrac{19}{x-19} = x^2 - 11x - 4$$ There are positive integers $a, b,$ and $c$ such that $m = a + \sqrt{b + \sqrt{c}}$. Find $a+b+c$.
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