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Problem 1 - Inequality

Source: 2020 Austrian National Competition for Advanced Students, Part 1 problem 1

June 6, 2020
inequalitiesthree variable inequalityAustriaalgebra

Problem Statement

Let x,yx, y and zz be positive real numbers such that x≥y+zx \geq y+z. Proof that x+yz+y+zx+z+xy≥7\frac{x+y}{z} + \frac{y+z}{x} +\frac{z+x}{y} \geq 7 When does equality occur?
(Walther Janous)
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