MathDB
Degree Six Polynomial's Roots

Source: 2014 AIME I Problem 14

March 14, 2014
quadraticsalgebrapolynomialsymmetrySFFTlinear algebraContrived

Problem Statement

Let mm be the largest real solution to the equation 3x−3+5x−5+17x−17+19x−19=x2−11x−4.\frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19}= x^2-11x-4. There are positive integers a,b,ca,b,c such that m=a+b+cm = a + \sqrt{b+\sqrt{c}}. Find a+b+ca+b+c.
Back to ProblemsView on AoPS