List questions from muirhead-inequality | MathQa

Prove the inequality $\frac{a^2+b^2}{c^2+a+b}+\frac{b^2+c^2}{a^2+b+c}+\frac{c^2+a^2}{b^2+c+a} \ge 2$

Published on 13 Jan 2025 - 5:27

Prove this inequality: $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}}\geq \sqrt{a}+\sqrt{b}+\sqrt{c}+3$

Published on 13 Jan 2025 - 5:36

Generalization of the AM-GM inequality for three variables

Published on 13 Jan 2025 - 5:28

Problematic inequality & hint

Published on 13 Jan 2025 - 5:46

How do we prove this inequality?

Published on 13 Jan 2025 - 5:42

Inequality in 4 variables Vasc's EV

Published on 13 Jan 2025 - 0:49

Prove that $\sum_\text{cyc} \frac{ab}{ab+b^2+ca}\le 1$

Published on 13 Jan 2025 - 5:37

Prove that $3 a^4+ 2 a^3 b - 3 a^2 b^2 - 2 a b^3 + 3 b^4\geq 0$.

Published on 13 Jan 2025 - 1:03

Prove an inequality : $\sum_{cyc}\frac{a^3}{abu+b^2v}\geq \frac{a+b+c}{u+v}$ without Jensen's inequality

Published on 13 Jan 2025 - 2:36

If $ab+bc+ca\ge1$, prove that $\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\ge\frac{\sqrt{3}}{abc}$

Published on 13 Jan 2025 - 5:15