{"status": "success", "data": {"description_md": "**POTD July 20, 2024**\n\nLet $a, b, c, x, y, z$ be real numbers such that:\n\n$$\\frac{x}{a} + \\frac{y}{b} + \\frac{z}{c} = 52$$\n\n$$\\frac{a}{x} + \\frac{b}{y} + \\frac{c}{z} = 147$$\n\n$$\\frac{xyz}{abc} = 9$$\n\nFind $\\left(\\dfrac{x}{a}\\right)^2 + \\left(\\dfrac{y}{b}\\right)^2 + \\left(\\dfrac{z}{c}\\right)^2$.", "description_html": "<p><strong>POTD July 20, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">a, b, c, x, y, z</span> be real numbers such that:</p>&#10;<p><span class=\"katex--display\">\\frac{x}{a} + \\frac{y}{b} + \\frac{z}{c} = 52</span></p>&#10;<p><span class=\"katex--display\">\\frac{a}{x} + \\frac{b}{y} + \\frac{c}{z} = 147</span></p>&#10;<p><span class=\"katex--display\">\\frac{xyz}{abc} = 9</span></p>&#10;<p>Find <span class=\"katex--inline\">\\left(\\dfrac{x}{a}\\right)^2 + \\left(\\dfrac{y}{b}\\right)^2 + \\left(\\dfrac{z}{c}\\right)^2</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #223", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}