MathDB

Problem 2 of Fourth round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018

algebrainequalities

Problem Statement

x

y

, and

z

are positive real numbers satisfying the equation

x+y+z=\frac{1}{x} + \frac{1}{y} + \frac{1}{z}

.
Prove the following inequality:

xy + yz + zx \geq 3