List questions from rearrangement-inequality | MathQa

Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$

Published on 13 Jan 2025 - 5:21

Find a maximum of: $x^{2016} \cdot y+y^{2016} \cdot z+z^{2016} \cdot x $

Published on 13 Jan 2025 - 5:36

How to show AM-GM inequality using rearrangement inequality?

Published on 12 Jan 2025 - 21:28

Inequality : $\frac{a}{\exp(a+b)}+\frac{b}{\exp(b+c)}+\frac{c}{\exp(c+a)}\leq \exp\Big(\frac{-2}{3}\Big)$

Published on 12 Jan 2025 - 21:37

Typical Olympiad Inequality? If $\sum_i^na_i=n$ with $a_i>0$, then $\sum_{i=1}^n\left(\frac{a_i^3+1}{a_i^2+1}\right)^4\geq n$

Published on 12 Jan 2025 - 21:43

An elegant but difficult inequality.

Published on 12 Jan 2025 - 21:10

The inequality $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{x+y}\ge \frac{3}{2}$

Published on 12 Jan 2025 - 21:28

Largest integer $k$ such that $\frac{a^{m+1}+b^{m+1}}{a^m+b^m}\geq\sqrt[k]{\frac{a^k+b^k}2}$

Published on 12 Jan 2025 - 21:36

Rearrangement inequality with infinite variables

Published on 12 Jan 2025 - 21:19

Proving an inequality involving fractions and square roots holds

Published on 12 Jan 2025 - 21:31