{"status": "success", "data": {"description_md": "If $x^2+y^2=25$ for real numbers $x$ and $y$, the minimum value of $$\\frac{50}{(7x)^{2}}+\\frac{(3x)^2}{y^2+25} $$ can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime, positive integers. Compute $m+n$.", "description_html": "<p>If <span class=\"katex--inline\">x^2+y^2=25</span> for real numbers <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span>, the minimum value of <span class=\"katex--display\">\\frac{50}{(7x)^{2}}+\\frac{(3x)^2}{y^2+25}</span> can be expressed as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime, positive integers. Compute <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Individuals A - Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsA-p08", "prev": "/problem/txo2024indivsA-p06"}}