Art of Problem Solving

AoPS Online

2014 AIME I Problems/Problem 14

Revision as of 17:27, 14 March 2014 by 1915933 (talk | contribs) (→‎Problem 14)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem 14

Let $m$ be the largest real solution to the equation

$\frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19}=x^2-11x-4$

There are positive integers $a$ , $b$ , and $c$ such that $m=a+\sqrt{b+\sqrt{c}}$ . Find $a+b+c$ .

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2014_AIME_I_Problems/Problem_14&oldid=60966"

© 2024 AoPS Incorporated