P2

Part of 2022 Junior Macedonian Mathematical Olympiad

Problems(1)

Inequality with one variable rational functions

Source: 2022 Junior Macedonian Mathematical Olympiad P2

a

b

c

be positive real numbers such that

a+b+c=3

. Prove the inequality

\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

inequalitiesalgebrarational functionfunction