List questions from muirhead-inequality

Published on 25 Mar 2026 - 12:54

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AM/GM inequalities

Published on 10 May 2026 - 17:35

287

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

Published on 15 Apr 2026 - 22:43

88

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How can I prove the this inequality?

Published on 15 Apr 2026 - 3:36

74

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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 16 Apr 2026 - 14:11

89

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Non - symetric inequality in 3 variables

Published on 31 Mar 2026 - 1:54

179

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

Published on 16 Apr 2026 - 2:41

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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 25 Mar 2026 - 12:50

62

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Proving Muirhead’s inequality by AM-GM

Published on 25 Mar 2026 - 12:52

140

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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 Mar 2026 - 11:16

294

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How to prove or disprove this algebraic inequality?

Published on 25 Mar 2026 - 11:11

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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 25 Mar 2026 - 12:50

105

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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 30 Mar 2026 - 5:15

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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 30 Mar 2026 - 5:17

1.4k

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

Published on 28 Apr 2026 - 16:36

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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