MathDB

1

Part of 2020 Federal Competition For Advanced Students, P1

Problems(1)

Problem 1 - Inequality

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

6/6/2020
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)
inequalitiesthree variable inequalityAustriaalgebra