ILL 1971 Problem 52

Prove the inequality $\frac{a_1+ a_3}{a_1 + a_2} + \frac{a_2 + a_4}{a_2 + a_3} + \frac{a_3 + a_1}{a_3 + a_4} + \frac{a_4 + a_2}{a_4 + a_1} \geq 4,$

where $a_i > 0, i = 1, 2, 3, 4.$

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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