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/volume8/exercise3.tex",3 "problem_type": "calculation",4 "problem": "问题2. 设方程 $x^2-2 \\sqrt{2} x+m=0$ 的两个虚根为 $\\alpha$ 、 $\\beta$, 且 $|\\alpha-\\beta|=1$, 则实数 $m$ 的值等于 ( ).\n(A) $-\\frac{1}{4}$\n(B) $\\frac{1}{4}$\n(C) $-\\frac{9}{4}$\n(D) $\\frac{9}{4}$",5 "solution": "D.\n由 $\\alpha+\\beta=2 \\sqrt{2},|\\alpha-\\beta|=1$, 而 $\\alpha-\\beta$ 是纯虚数, 从而 $\\alpha-\\beta= \\pm \\mathrm{i}$.\n$$\n4 \\alpha \\beta=(\\alpha+\\beta)^2-(\\alpha-\\beta)^2=(2 \\sqrt{2})^2+1=9 \\text {, 所以 } m=\\alpha \\beta=\\frac{9}{4} \\text {. }\n$$",6 "remark": "",7 "figures": []8}