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Regional Olympiad - FBH 2013 Grade 12 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013

September 24, 2018

algebraInequality

Problem Statement

a

b

and

c

are nonnegative real numbers such that

a^2+b^2+c^2=1

, prove that

\frac{1}{2} \leq \frac{a}{1+a^4}+\frac{b}{1+b^4}+\frac{c}{1+c^4} \leq \frac{9\sqrt{3}}{10}