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Found problems: 1

2022 Indonesia TST, A
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 $a^2 + b$. [i]Proposed by Fajar Yuliawan[/i]
minimum inequalities inequality asymmetric algebra AM-GM inequality