MathDB

n-variable inequality

Source: All-Russian MO 2023 Final stage 10.8

April 23, 2023

inequalitiesalgebra

Problem Statement

Given is a real number

a \in (0,1)

and positive reals

x_0, x_1, \ldots, x_n

such that

\sum x_i=n+a

and

\sum \frac{1}{x_i}=n+\frac{1}{a}

. Find the minimal value of

\sum x_i^2