olymmath

BALTIC-WAY 1997 Problem 4

    Prove that the arithmetic mean aa of x1,…,xnx_{1}, \ldots, x_{n} satisfies

    (x1−a)2+⋯+(xn−a)2⩽12(∣x1−a∣+⋯+∣xn−a∣)2.\left(x_{1}-a\right)^{2}+\cdots+\left(x_{n}-a\right)^{2} \leqslant \frac{1}{2}\left(\left|x_{1}-a\right|+\cdots+\left|x_{n}-a\right|\right)^{2} .

    Dataset text NuminaMath olympiads. Quoted with source.

    Solutions

    No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

    Add a solution

    Locator baltic-way/1997/p4 · Tag YYSTFYM0S0 · Edit this page on GitHub · Keys: j next, k previous