List questions from a-m-g-m-inequality | MathQA

Show that $x^{\frac1x}<1.5$ for $x \in \mathbb R$

Published on 17 Dec 2022 - 13:00

Prove or disprove that the inequality is valid if $x,y,z$ are positive numbers and $xyz=1$.

Published on 28 Mar 2026 - 2:24

Prove or disprove the inequality if $a,b,c>0$, $a \geq b+c$.

Published on 28 Mar 2026 - 2:23

Why does the AM-GM inequality not show $25 \csc^2(\theta) +16 \sin^2(\theta)$ has a minimum of $41$ as the graph indicates?

Published on 28 Dec 2022 - 4:32

$\left\{(x_1,x_2)\mid \left|f(x_1,x_2)-f(0,0)\right|<\frac{1}{2}\right\}=\left\{(0,0)\right\}\cup\left\{(x_1,x_2)\mid x_1\neq\pm x_2\right\}$

Published on 31 Dec 2022 - 22:49

Proof or references for strengthened AM-GM

Published on 01 Jan 2023 - 23:52

For $x,y,z∈ℝ^{+}$,without using Hölder's inequality prove that $\frac{x}{\sqrt{x^2+8yz}}+\frac{y}{\sqrt{y^2+8xz}}+\frac{z}{\sqrt{z^2+8xy}}\geq1$.

Published on 27 Mar 2026 - 23:48

AM-GM & Minimization Proof

Published on 13 Jan 2023 - 4:08

JBMO-$2014$ Inequality question

Published on 27 Mar 2026 - 10:06

If $xy+yz+zx=3$ and $x,y,z\geq0$, prove that: $\frac{1}{1+3x-p}+\frac{1}{1+3y-p}+\frac{1}{1+3z-p}\leq\frac{3}{1+2p}$

Published on 21 Jan 2023 - 18:14