{"status": "success", "data": {"description_md": "If the minimum value of $\\sqrt{x^2 - 6x + 36} + \\sqrt{x^2 - 8x + 64}$ for positive $x$ can be represented as $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime, compute $a+b$.", "description_html": "<p>If the minimum value of <span class=\"katex--inline\">\\sqrt{x^2 - 6x + 36} + \\sqrt{x^2 - 8x + 64}</span> for positive <span class=\"katex--inline\">x</span> can be represented as <span class=\"katex--inline\">a\\sqrt{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are positive integers and <span class=\"katex--inline\">b</span> is not divisible by the square of any prime, compute <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "March Break 2024 - Problem 11", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}