MathDB

2014 Algebra #7: Inequality involving Median

Source:

July 7, 2014

inequalities

Problem Statement

Find the largest real number

c

such that

\sum_{i=1}^{101}x_i^2\geq cM^2

whenever

x_1,\ldots,x_{101}

are real numbers such that

x_1+\cdots+x_{101}=0

and

M

is the median of

x_1,\ldots,x_{101}