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Problem 4 of Finals

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

January 11, 2020

algebraInequalityinequalitiesHigh school olympiadinequalities proposed

Problem Statement

For all real numbers

a,b,c>0

such that

abc=1

, prove that

\frac{a}{1+b^3}+\frac{b}{1+c^3}+\frac{c}{1+a^3}\geq \frac{3}{2}