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2022 AMC 10BProblem 5P1-10~2 minPrint
Algebraic ManipulationExponents, Logarithms & RadicalsApply an identity: SFFT, sum of squares, difference of cubes, Vieta

What is the value of (1+13)(1+15)(1+17)(1−132)(1−152)(1−172)?\frac{\left(1+\frac13\right)\left(1+\frac15\right)\left(1+\frac17\right)}{\sqrt{\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{5^2}\right)\left(1-\frac{1}{7^2}\right)}}?

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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.