olymmath

USAJMO 2014 Problem 1

  • Day 1

Let aa , bb , cc be real numbers greater than or equal to 11 . Prove that min⁡(10a2−5a+1b2−5b+10,10b2−5b+1c2−5c+10,10c2−5c+1a2−5a+10)≤abc.\min \left(\frac{10a^2-5a+1}{b^2-5b+10},\frac{10b^2-5b+1}{c^2-5c+10},\frac{10c^2-5c+1}{a^2-5a+10}\right )\leq abc.

Dataset text AI-MO AoPS. Quoted with source.

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