{"status": "success", "data": {"description_md": "Let $x$ and $y$ be real numbers such that\n\n$$\\log_{25} x = \\log_{20} y = \\log_{16} (24x-20y).$$\n\nGiven that the value of $\\sqrt{6-\\frac{5y}{x}}$ can be written as $\\sqrt{a}-b$ for positive integers $a$ and $b$ where $a$ is not divisible by the square of any prime, find $a+b$.", "description_html": "<p>Let <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span> be real numbers such that</p>&#10;<p><span class=\"katex--display\">\\log_{25} x = \\log_{20} y = \\log_{16} (24x-20y).</span></p>&#10;<p>Given that the value of <span class=\"katex--inline\">\\sqrt{6-\\frac{5y}{x}}</span> can be written as <span class=\"katex--inline\">\\sqrt{a}-b</span> for positive integers <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> where <span class=\"katex--inline\">a</span> is not divisible by the square of any prime, find <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Holiday Contest 2025 - Guts Round - Set 3 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}