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Another amazing inequality

Source: Kyiv City MO 2021 Round 1, Problem 11.4

December 21, 2023
inequalitiesalgebrainequalities proposed

Problem Statement

For positive real numbers a,b,ca, b, c with sum 32\frac{3}{2}, find the smallest possible value of the following expression:
a3bc+b3ca+c3ab+1abc\frac{a^3}{bc} + \frac{b^3}{ca} + \frac{c^3}{ab} + \frac{1}{abc}
Proposed by Serhii Torba
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