MathDB

Bosnia and Herzegovina JBMO TST 2016 Problem 4

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2016

September 16, 2018

algebrainequalities

Problem Statement

Let

x

y

and

z

be positive real numbers such that

\sqrt{xy} + \sqrt{yz} + \sqrt{zx} = 3

. Prove that

\sqrt{x^3+x} + \sqrt{y^3+y} + \sqrt{z^3+z} \geq \sqrt{6(x+y+z)}