MathDB

A11

Part of 2021-IMOC

Problems(1)

Hard Inequality with reals

Source: IMOC 2021 A11

8/11/2021
Given n≥2n \geq 2 reals x1,x2,…,xn.x_1 , x_2 , \dots , x_n. Show that ∏1≤i<j≤n(xi−xj)2≤∏i=0n−1(∑j=1nxj2i)\prod_{1\leq i < j \leq n} (x_i - x_j)^2 \leq \prod_{i=0}^{n-1} \left(\sum_{j=1}^{n} x_j^{2i}\right) and find all the (x1,x2,…,xn)(x_1 , x_2 , \dots , x_n) where the equality holds.
inequalities