{"status": "success", "data": {"description_md": "Let $P(x)=x^2-3x-9$. A real number $x$ is chosen at random from the interval $5\\leq x \\leq 15$. The probability that $\\lfloor \\sqrt{P(x)} \\rfloor = \\sqrt{P(\\lfloor x \\rfloor )}$ is equal to $\\dfrac{\\sqrt{a}+\\sqrt{b}+\\sqrt{c}-d}{e}$, where $a,b,c,d$ and $e$ are positive integers and none of $a,b,$ or $c$ is divisible by the square of a prime. Find $a+b+c+d+e$.\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\">P(x)=x^2-3x-9</span>. A real number <span class=\"katex--inline\">x</span> is chosen at random from the interval <span class=\"katex--inline\">5\\leq x \\leq 15</span>. The probability that <span class=\"katex--inline\">\\lfloor \\sqrt{P(x)} \\rfloor = \\sqrt{P(\\lfloor x \\rfloor )}</span> is equal to <span class=\"katex--inline\">\\dfrac{\\sqrt{a}+\\sqrt{b}+\\sqrt{c}-d}{e}</span>, where <span class=\"katex--inline\">a,b,c,d</span> and <span class=\"katex--inline\">e</span> are positive integers and none of <span class=\"katex--inline\">a,b,</span> or <span class=\"katex--inline\">c</span> is divisible by the square of a prime. Find <span class=\"katex--inline\">a+b+c+d+e</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": "2011 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/11_aime_II_p14"}}