math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
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1{2 "source_file": "./raw_volume-zh/volume4/exercise2.tex",3 "problem_type": "calculation",4 "problem": "问题13. 求乘积 $x^2 y^2 z^2 u$ 在条件 $x, y, z, u \\geqslant 0$ 与 $2 x+x y+z+y z u=1$ 下的最大值.",5 "solution": "由平均值不等式, 得 $\\sqrt[4]{2 x^2 y^2 z^2 u} \\leqslant \\frac{2 x+x y+z+z y u}{4}=\\frac{1}{4}$, 即\n$x^2 y^2 z^2 u \\leqslant \\frac{1}{512}$. 而且当 $2 x=x y=z=y z u=\\frac{1}{4}$, 即 $x=\\frac{1}{8}, y=2, z==\\frac{1}{4}$, $u=\\frac{1}{2}$ 时等式成立.\n于是, 所求的最大值为 $\\frac{1}{512}$.",6 "remark": "",7 "figures": []8}