NL-NWO 1991 Problem 1

Prove that for any three positive real numbers $a,b,c, \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a} \ge \frac{9}{2} \cdot \frac{1}{a+b+c}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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