{"status": "success", "data": {"description_md": "Let $x$, $y$, and $z$ be real numbers satisfying the system of equations\n$xy+4z=60$\n$yz+4x=60$\n$zx+4y=60.$\nLet $S$ be the set of possible values of $x$. Find the sum of the squares of the elements of $S$.\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\">x</span>, <span class=\"katex--inline\">y</span>, and <span class=\"katex--inline\">z</span> be real numbers satisfying the system of equations<br/>&#10;<span class=\"katex--inline\">xy+4z=60</span><br/>&#10;<span class=\"katex--inline\">yz+4x=60</span><br/>&#10;<span class=\"katex--inline\">zx+4y=60.</span><br/>&#10;Let <span class=\"katex--inline\">S</span> be the set of possible values of <span class=\"katex--inline\">x</span>. Find the sum of the squares of the elements of <span class=\"katex--inline\">S</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": 3, "problem_name": "2023 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/23_aime_II_p05", "prev": "/problem/23_aime_II_p03"}}