Home Competitions AMO-Bench 2025 Problem 11
AMO-Bench 2025 Problem 11
Let x 1 , x 2 , … , x n x_{1}, x_{2}, \ldots, x_{n} x 1 , x 2 , … , x n x 1 + x 2 + ⋯ + x n = n . x_{1} + x_{2} + \cdots + x_{n} = n. x 1 + x 2 + ⋯ + x n = n . n n n 1 x 1 2 + 1 x 2 2 + ⋯ + 1 x n 2 ≥ x 1 2 + x 2 2 + ⋯ + x n 2 . \frac{1}{x_{1}^{2}} + \frac{1}{x_{2}^{2}} + \cdots + \frac{1}{x_{n}^{2}}
\;\geq x_{1}^{2} + x_{2}^{2} + \cdots + x_{n}^{2}. x 1 2 1 + x 2 2 1 + ⋯ + x n 2 1 ≥ x 1 2 + x 2 2 + ⋯ + x n 2 .
Dataset text AMO-Bench . Open licence.
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