{"status": "success", "data": {"description_md": "If $$a^3b^2c = 108$$ for $a, b, c \\in \\mathbb{R}^+$, find $\\min(2a+b+8c+5)$.", "description_html": "<p>If <span class=\"katex--display\">a^3b^2c = 108</span> for <span class=\"katex--inline\">a, b, c \\in \\mathbb{R}^+</span>, find <span class=\"katex--inline\">\\min(2a+b+8c+5)</span>.</p>&#10;", "hints_md": "Try to split $2a$ into $3$ terms, and $b$ into $2$ terms. Then, apply AM-GM. Do **NOT** put $5$ into the inequality.", "hints_html": "<p>Try to split <span class=\"katex--inline\">2a</span> into <span class=\"katex--inline\">3</span> terms, and <span class=\"katex--inline\">b</span> into <span class=\"katex--inline\">2</span> terms. Then, apply AM-GM. Do <strong>NOT</strong> put <span class=\"katex--inline\">5</span> into the inequality.</p>&#10;", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Silver II", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}