MathDB

Hard inequality

Source: Russian TST 2022, Day 8 P3

March 21, 2023

algebraInequality

Problem Statement

Let

n\geqslant 3

be an integer and

x_1>x_2>\cdots>x_n

be real numbers. Suppose that

x_k>0\geqslant x_{k+1}

for an index

k{}

. Prove that

\sum_{i=1}^k\left(x_i^{n-2}\prod_{j\neq i}\frac{1}{x_i-x_j}\right)\geqslant 0.