INMO 1988 Problem 4

If $a$ and $b$ are positive and $a + b = 1$ , prove that $\left(a+\frac{1}{a}\right)^2+\left(b+\frac{1}{b}\right)^2 \geq \frac{25}{2}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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