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ab(1 - a)(1 - b)/(1- ab)^2 < 14 - All-Russian MO 1996 Regional (R4) 9.7

Source:

September 23, 2024
algebrainequalities

Problem Statement

Prove that if 0<a,b<1,0 < a, b < 1, then ab(1−a)(1−b)(1−ab)2<14.\frac{ab(1 - a)(1 - b)}{(1- ab)^2 }< \frac14.
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