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Inequality with one variable rational functions

Source: 2022 Junior Macedonian Mathematical Olympiad P2

June 7, 2022
inequalitiesalgebrarational functionfunction

Problem Statement

Let aa, bb and cc be positive real numbers such that a+b+c=3a+b+c=3. Prove the inequality a3a2+1+b3b2+1+c3c2+1≥32.\frac{a^3}{a^2+1}+\frac{b^3}{b^2+1}+\frac{c^3}{c^2+1} \geq \frac{3}{2}.
Proposed by Anastasija Trajanova
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