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an inequality about geometric average

Source: 2021ChinaTST test3 day1 P3

April 13, 2021
inequalitiesalgebraTSTChina TST

Problem Statement

Determine the greatest real number C C , such that for every positive integer n≥2 n\ge 2 , there exists x1,x2,...,xn∈[−1,1] x_1, x_2,..., x_n \in [-1,1], so that ∏1≤i<j≤n(xi−xj)≥Cn(n−1)2\prod_{1\le i<j\le n}(x_i-x_j) \ge C^{\frac{n(n-1)}{2}}.
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