{"status": "success", "data": {"description_md": "**POTD June 13, 2024**\n\nGiven that $x = \\frac{4z^2}{4z^2+1}, y = \\frac{4x^2}{4x^2+1},$ and $z = \\frac{4y^2}{4y^2+1}$, where $x$, $y$, and $z$ are real numbers, find twice the sum of all possible values of $x$.", "description_html": "<p><strong>POTD June 13, 2024</strong></p>&#10;<p>Given that <span class=\"katex--inline\">x = \\frac{4z^2}{4z^2+1}, y = \\frac{4x^2}{4x^2+1},</span> and <span class=\"katex--inline\">z = \\frac{4y^2}{4y^2+1}</span>, where <span class=\"katex--inline\">x</span>, <span class=\"katex--inline\">y</span>, and <span class=\"katex--inline\">z</span> are real numbers, find twice the sum of all possible values of <span class=\"katex--inline\">x</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #186", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}