{"status": "success", "data": {"description_md": "Given\n\n$$x=3+\\dfrac{2x^2-1}{3+\\dfrac{2x^3-x}{3x+2x^2-1}} $$\n\nthe largest real solution can be written as $\\frac{\\sqrt a - b}{c}$, where $a,b,$ and $c$ are positive integers with $a$ not divisible by the square of any prime. Compute $a+b+c$.", "description_html": "<p>Given</p>&#10;<p><span class=\"katex--display\">x=3+\\dfrac{2x^2-1}{3+\\dfrac{2x^3-x}{3x+2x^2-1}}</span></p>&#10;<p>the largest real solution can be written as <span class=\"katex--inline\">\\frac{\\sqrt a - b}{c}</span>, where <span class=\"katex--inline\">a,b,</span> and <span class=\"katex--inline\">c</span> are positive integers with <span class=\"katex--inline\">a</span> not divisible by the square of any prime. Compute <span class=\"katex--inline\">a+b+c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "TxO Math Bowl 2024 - Guts Contest - Set 7 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}