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American Shortlist Inequality

Source: IMO Shortlist 1993, USA 3

October 24, 2005
inequalitiesfunctionfour variables4-variable inequalityalgebraIMO Shortlist

Problem Statement

Prove that ab+2c+3d+bc+2d+3a+cd+2a+3b+da+2b+3c≥23 \frac{a}{b+2c+3d} +\frac{b}{c+2d+3a} +\frac{c}{d+2a+3b}+ \frac{d}{a+2b+3c} \geq \frac{2}{3} for all positive real numbers a,b,c,da,b,c,d.
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