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2024 AMC 10BProblem 9P1-10~2 minPrint
Algebraic ManipulationApply an identity: SFFT, sum of squares, difference of cubes, VietaTest small/specific values or special cases to find or verify the answer

Real numbers a,b,a, b, and cc have arithmetic mean 00 . The arithmetic mean of a2,b2,a^2, b^2, and c2c^2 is 1010 . What is the arithmetic mean of ab,ac,ab, ac, and bcbc ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.