ILL 1970 Problem 1

Prove that $\frac{ab}{a+b}+\frac{bc}{b+c}+\frac{ca}{c+a}\le \frac{a+b+c}{2}$ , where $a,b,c\in\mathbb{R}^{+}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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