{"status": "success", "data": {"description_md": "Let $a, b, c,$ and $d$ be real numbers that satisfy the system of equations$a+b=-3$\n$ab+bc+ca= -4$\n$abc+bcd+cda+dab=14$\n$abcd=30.$\nThere exist relatively prime positive integers $m$ and $n$ such that\n$$a^2 + b^2 + c^2 + d^2 = \\frac{m}{n}. $$Find $m + n$.\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\">a, b, c,</span> and <span class=\"katex--inline\">d</span> be real numbers that satisfy the system of equations<span class=\"katex--inline\">a+b=-3</span><br/>&#10;<span class=\"katex--inline\">ab+bc+ca= -4</span><br/>&#10;<span class=\"katex--inline\">abc+bcd+cda+dab=14</span><br/>&#10;<span class=\"katex--inline\">abcd=30.</span><br/>&#10;There exist relatively prime positive integers <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> such that<br/>&#10;<span class=\"katex--display\">a^2 + b^2 + c^2 + d^2 = \\frac{m}{n}. </span>Find <span class=\"katex--inline\">m + n</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2021 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_II_p08", "prev": "/problem/21_aime_II_p06"}}