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Asymmetric Weighted Inequality

Source: Indonesian Stage 1 TST for IMO 2022, Test 3 (Algebra)

December 25, 2021
algebraInequalityasymmetricminimuminequalities

Problem Statement

Let aa and bb be two positive reals such that the following inequality ax3+by2≥xy−1 ax^3 + by^2 \geq xy - 1 is satisfied for any positive reals x,y≥1x, y \geq 1. Determine the smallest possible value of a2+ba^2 + b.
Proposed by Fajar Yuliawan
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