Problem

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

Tags: algebra, Inequality, asymmetric, minimum, inequalities



Let $a$ and $b$ be two positive reals such that the following inequality \[ ax^3 + by^2 \geq xy - 1 \]is satisfied for any positive reals $x, y \geq 1$. Determine the smallest possible value of $a^2 + b$. Proposed by Fajar Yuliawan