olymmath

JBMO-SL 2004 A4

Prove that if 0<ab<b<2a0<\frac{a}{b}<b<2 a then

2ab−a27ab−3b2−2a2+2ab−b27ab−3a2−2b2≥1+14(ab−ba)2\frac{2 a b-a^{2}}{7 a b-3 b^{2}-2 a^{2}}+\frac{2 a b-b^{2}}{7 a b-3 a^{2}-2 b^{2}} \geq 1+\frac{1}{4}\left(\frac{a}{b}-\frac{b}{a}\right)^{2}

Dataset text NuminaMath olympiads. Quoted with source.

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