List questions from muirhead-inequality

Published on 14 Jul 2020 - 12:26

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AM/GM inequalities

Published on 25 Mar 2026 - 9:25

284

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Prove this inequality $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$

Published on 24 Aug 2016 - 3:26

84

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How can I prove the this inequality?

Published on 11 Sep 2016 - 4:32

71

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How to prove this $\sum\limits_{cyc}a\sqrt{b^2+(n^2-1)c^2}\le (a+b+c)^2+(n-3)(ab+bc+ca)$

Published on 20 Oct 2016 - 12:39

87

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Non - symetric inequality in 3 variables

Published on 23 Oct 2016 - 10:36

176

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Prove that $\frac1{a+b+1}+\frac1{b+c+1}+\frac1{c+a+1}\le1$

Published on 07 Dec 2016 - 5:04

107

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a,b,c>0 and prove $\frac{a}{a+\sqrt{(a+2b)(a+2c)}}+\frac{b}{b+\sqrt{(b+2a)(b+2c)}}+\frac{c}{c+\sqrt{(c+2b)(c+2a)}}\le \frac{3}{4}.$

Published on 18 Jul 2023 - 0:36

61

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Proving Muirhead’s inequality by AM-GM

Published on 20 Jul 2023 - 18:15

139

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Prove $\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a}\ge \sqrt{2(ab+bc+ca)+12}$ when $a+b+c=3.$

Published on 25 Nov 2023 - 8:36

293

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How to prove or disprove this algebraic inequality?

Published on 23 Apr 2015 - 8:38

477

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How to prove that $\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\leq\frac{3\sqrt{3}}{4}$?

Published on 03 May 2015 - 10:18

104

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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 21 Feb 2016 - 8:51

320

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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 21 Apr 2016 - 3:10

1.4k

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What is majorization, and how is it related to Muirhead's inequalities?

Published on 14 Mar 2026 - 14:15

List Question

Proof of inequality by Muirhead

AM/GM inequalities

Prove this inequality $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$

How can I prove the this inequality?

How to prove this $\sum\limits_{cyc}a\sqrt{b^2+(n^2-1)c^2}\le (a+b+c)^2+(n-3)(ab+bc+ca)$

Non - symetric inequality in 3 variables

Prove that $\frac1{a+b+1}+\frac1{b+c+1}+\frac1{c+a+1}\le1$

a,b,c>0 and prove $\frac{a}{a+\sqrt{(a+2b)(a+2c)}}+\frac{b}{b+\sqrt{(b+2a)(b+2c)}}+\frac{c}{c+\sqrt{(c+2b)(c+2a)}}\le \frac{3}{4}.$

Proving Muirhead’s inequality by AM-GM

Prove $\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a}\ge \sqrt{2(ab+bc+ca)+12}$ when $a+b+c=3.$

How to prove or disprove this algebraic inequality?

How to prove that $\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\leq\frac{3\sqrt{3}}{4}$?

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

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

What is majorization, and how is it related to Muirhead's inequalities?

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