Question

Proving $(a+b+c)^2\prod_{cyc}(a+b)-4\sum_{cyc}(a^2b+a^2c)\sum_{cyc}ab\geqq 0$

score 126 · Answer 1 · 2026-03-25 14:26:47

126

Views

Proving $(a+b+c)^2\prod_{cyc}(a+b)-4\sum_{cyc}(a^2b+a^2c)\sum_{cyc}ab\geqq 0$

Published on 25 Mar 2026 - 14:26

score 182 · Answer 2 · 2026-03-25 12:50:04

182

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Prove $\frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b} +\frac{81abc}{4(a+b+c)^2} \geqq \frac{7}{4} (a+b+c)$

Published on 25 Mar 2026 - 12:50

score 83 · Answer 3 · 2026-03-25 10:58:45

83

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Combinatorics for exterior power for arbitrary Specht module

Published on 25 Mar 2026 - 10:58

score 161 · Answer 4 · 2026-03-25 17:44:36

161

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Prove the following inequality $\sum_{i<j<k}\frac{a_ia_ja_k}{(n-2)(n-1)n}\le \bigg(\sum_{i<j}\frac{a_ia_j}{(n-1)n}\bigg)^2+\frac{1}{12}$

Published on 25 Mar 2026 - 17:44

score 142 · Answer 5 · 2020-05-19 12:11:10

142

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Find minimal value of $\left(2-x\right)\left(2-y\right)\left(2-z\right)$

Published on 19 May 2020 - 12:11

score 138 · Answer 6 · 2026-03-25 16:02:18

138

Views

Prove $(a+b+c)^3 (a+b-c)(b+c-a)(c+a-b) \leqq 27a^2 b^ 2 c^2$

Published on 25 Mar 2026 - 16:02

score 199 · Answer 7 · 2026-03-25 14:25:08

199

Views

Prove $\frac{x^2+yz}{\sqrt{2x^2(y+z)}}+\frac{y^2+zx}{\sqrt{2y^2(z+x)}}+\frac{z^2+xy}{\sqrt{2z^2(x+y)}}\geqq 1$

Published on 25 Mar 2026 - 14:25

score 697 · Answer 8 · 2020-05-21 05:55:24

697

Views

Prove Newton's Identities using the properties of a symmetric polynomial.

Published on 21 May 2020 - 5:55

score 126 · Answer 9 · 2020-05-24 01:05:11

126

Views

Find the stronger inequality of $\frac{1}{ab+2c^{2}+2c}+\frac{1}{bc+2a^{2}+2a}+\frac{1}{ca+2b^{2}+2b}\geq \frac{1}{\sum ab}$

Published on 24 May 2020 - 1:05

score 164 · Answer 10 · 2026-03-25 17:29:46

164

Views

Proving inequality by SOS.

Published on 25 Mar 2026 - 17:29

score 48 · Answer 11 · 2026-03-25 19:05:47

48

Views

Writing explicitly $(s^2-1)^2+(t^2-1)^2$ as a polynomial in $st$ and $s+t$?

Published on 25 Mar 2026 - 19:05

score 24 · Answer 12 · 2026-03-25 19:00:19

24

Views

Symmetric functions for multidimensional variables

Published on 25 Mar 2026 - 19:00

score 83 · Answer 13 · 2020-05-30 06:42:14

$\min\left(\sum_{\text{sym}}\frac{(2x^2+y)(4x + y^2)}{\underset{\ne0}{(2x + y - 2)^2}} - 3(\underset{\gt0}{x}+\underset{\gt0}{y})\right)=?$

score 601 · Answer 14 · 2026-03-25 11:03:43

601

Views

Using symmetric polynomials to find the discriminant of $x^4 + px + q$ over $\mathbb{Q}$

Published on 25 Mar 2026 - 11:03

score 103 · Answer 15 · 2026-03-26 20:58:28

103

Views

Inequality question.

Published on 26 Mar 2026 - 20:58

List Question

Proving $(a+b+c)^2\prod_{cyc}(a+b)-4\sum_{cyc}(a^2b+a^2c)\sum_{cyc}ab\geqq 0$

Prove $\frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b} +\frac{81abc}{4(a+b+c)^2} \geqq \frac{7}{4} (a+b+c)$

Combinatorics for exterior power for arbitrary Specht module

Prove the following inequality $\sum_{i<j<k}\frac{a_ia_ja_k}{(n-2)(n-1)n}\le \bigg(\sum_{i<j}\frac{a_ia_j}{(n-1)n}\bigg)^2+\frac{1}{12}$

Find minimal value of $\left(2-x\right)\left(2-y\right)\left(2-z\right)$

Prove $(a+b+c)^3 (a+b-c)(b+c-a)(c+a-b) \leqq 27a^2 b^ 2 c^2$

Prove $\frac{x^2+yz}{\sqrt{2x^2(y+z)}}+\frac{y^2+zx}{\sqrt{2y^2(z+x)}}+\frac{z^2+xy}{\sqrt{2z^2(x+y)}}\geqq 1$

Prove Newton's Identities using the properties of a symmetric polynomial.

Find the stronger inequality of $\frac{1}{ab+2c^{2}+2c}+\frac{1}{bc+2a^{2}+2a}+\frac{1}{ca+2b^{2}+2b}\geq \frac{1}{\sum ab}$

Proving inequality by SOS.

Writing explicitly $(s^2-1)^2+(t^2-1)^2$ as a polynomial in $st$ and $s+t$?

Symmetric functions for multidimensional variables

$\min\left(\sum_{\text{sym}}\frac{(2x^2+y)(4x + y^2)}{\underset{\ne0}{(2x + y - 2)^2}} - 3(\underset{\gt0}{x}+\underset{\gt0}{y})\right)=?$

Using symmetric polynomials to find the discriminant of $x^4 + px + q$ over $\mathbb{Q}$

Inequality question.

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