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Bosnia and Herzegovina TST 1998 Day 1 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 1998

September 20, 2018

algebraInequalityinequalities

Problem Statement

For positive real numbers

x

y

and

z

holds

x^2+y^2+z^2=1

. Prove that

\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2} \leq \frac{3\sqrt{3}}{4}