Maths Olympiad Prep

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Algebra Difficulty 5.0 AIME, harder Prove it United Kingdom

For each positive real number xx, we define {x}\{x\} to be the greater of xx and 1/x1/x, with {1}=1\{1\} = 1. Find, with proof, all positive real numbers yy such that 5y{8y}{25y}=1.5y\{8y\}\{25y\} = 1.

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