{"status": "success", "data": {"description_md": "**POTD March 23, 2024**\n\nLet $x_1$ and $x_2$ be the roots of the equation $y = \\left|3-2\\sqrt{-4x^2+24x-27}\\right|$. Let $m$ be the value of the global maximum of this graph (no calculus needed). If the value of $m\\cdot\\left|x_1-x_2\\right|$ can be expressed as $\\frac{a\\sqrt{b}}{c}$, where $a, b,$ and $c$ are positive integers, $\\gcd{(a, c)} = 1$, and $c$ is not divisible by the square of any prime, find $a+b+c$.", "description_html": "<p><strong>POTD March 23, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">x_1</span> and <span class=\"katex--inline\">x_2</span> be the roots of the equation <span class=\"katex--inline\">y = \\left|3-2\\sqrt{-4x^2+24x-27}\\right|</span>. Let <span class=\"katex--inline\">m</span> be the value of the global maximum of this graph (no calculus needed). If the value of <span class=\"katex--inline\">m\\cdot\\left|x_1-x_2\\right|</span> can be expressed as <span class=\"katex--inline\">\\frac{a\\sqrt{b}}{c}</span>, where <span class=\"katex--inline\">a, b,</span> and <span class=\"katex--inline\">c</span> are positive integers, <span class=\"katex--inline\">\\gcd{(a, c)} = 1</span>, and <span class=\"katex--inline\">c</span> is not divisible by the square of any prime, find <span class=\"katex--inline\">a+b+c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #105", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}