{"status": "success", "data": {"description_md": "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 $a,b,c$ such that $m = a + \\sqrt{b+\\sqrt{c}}$. Find $a+b+c$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let <span class=\"katex--inline\">m</span> be the largest real solution to the equation <span class=\"katex--display\">\\frac{3}{x-3}+\\frac{5}{x-5}+\\frac{17}{x-17}+\\frac{19}{x-19}= x^2-11x-4.</span> There are positive integers <span class=\"katex--inline\">a,b,c</span> such that <span class=\"katex--inline\">m = a + \\sqrt{b+\\sqrt{c}}</span>. Find <span class=\"katex--inline\">a+b+c</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2014 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/14_aime_I_p15", "prev": "/problem/14_aime_I_p13"}}