Question

Can't understand proof of fundamental theorem of symmetric polynomials

score 534 · Answer 1 · 2023-10-28 03:42:44

534

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Can't understand proof of fundamental theorem of symmetric polynomials

Published on 28 Oct 2023 - 3:42

score 62 · Answer 2 · 2023-10-29 21:58:42

62

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Schur $Q-$functions

Published on 29 Oct 2023 - 21:58

score 516 · Answer 3 · 2023-10-30 14:16:52

516

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Finding $\small{\max\limits_{ab+bc+ca=1}\dfrac{\sqrt{a+bc}+\sqrt{b+ca}+\sqrt{c+ab}}{\sqrt{3a+3b+3c+10}} }$

Published on 30 Oct 2023 - 14:16

score 68 · Answer 4 · 2023-11-02 03:24:26

68

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What's the name for this method of putting the roots of a polynomial in a system of equations?

Published on 02 Nov 2023 - 3:24

score 133 · Answer 5 · 2026-03-26 04:36:27

133

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Prove $\frac{a}{\sqrt{4a+3bc}}+\frac{b}{\sqrt{4b+3ca}}+\frac{c}{\sqrt{4c+3ab}}\le \frac{\sqrt{a+b+c+2}}{2}.$

Published on 26 Mar 2026 - 4:36

score 85 · Answer 6 · 2026-03-26 04:36:33

85

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Prove that $\frac{1}{\sqrt{4a+bc}}+\frac{1}{\sqrt{4b+ca}}+\frac{1}{\sqrt{4c+ab}}\le \sqrt{2(a+b+c)}.$

Published on 26 Mar 2026 - 4:36

score 39 · Answer 7 · 2026-02-23 06:34:47

39

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inverting the first three elementary symmetric polynomials

Published on 23 Feb 2026 - 6:34

score 601 · Answer 8 · 2023-11-07 03:40:42

601

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Minimizing $ \sum\limits_{cyc}\frac{\sqrt{5a+8bc}}{8a+5bc}$ with $ \sum\limits_{cyc}ab=1$

Published on 07 Nov 2023 - 3:40

score 61 · Answer 9 · 2023-11-08 08:43:00

61

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Prove $\sqrt{a+b-2ab}+\sqrt{c+b-2bc}+\sqrt{a+c-2ca}\ge 2\sqrt{a+b+c-1}.$

Published on 08 Nov 2023 - 8:43

score 112 · Answer 10 · 2026-03-26 04:36:27

112

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Prove $\sqrt{\frac{a+b}{c+ab}}+\sqrt{\frac{c+b}{a+cb}}+\sqrt{\frac{a+c}{b+ac}}\ge 3,$ if $ab+bc+ca=3.$

Published on 26 Mar 2026 - 4:36

score 75 · Answer 11 · 2026-03-26 04:36:23

75

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$\sum \frac{a^2+b^2}{c^2}-\frac{7}{2} \geq \sqrt[3]{\prod \left(\frac{a}{b+c}+\frac{1}{3}\right)}$ for a,b,c real

Published on 26 Mar 2026 - 4:36

score 98 · Answer 12 · 2023-11-13 17:26:58

98

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Prove that tan($Z$) = $\frac{e_1t - e_3t^3 + e_5t^5 - \cdots}{1 - e_2t^2 + e_4t^4 - \cdots}$

Published on 13 Nov 2023 - 17:26

score 90 · Answer 13 · 2026-03-26 16:14:03

90

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What are the generators of polynomials symmetric under a subgroup of the permutation group

Published on 26 Mar 2026 - 16:14

score 471 · Answer 14 · 2026-03-25 18:48:12

471

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How to prove $ a+b+c+\sqrt{bc}+\sqrt{ca}+\sqrt{ab}\ge 6$?

Published on 25 Mar 2026 - 18:48

score 89 · Answer 15 · 2026-03-26 08:02:29

89

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Prove $\color{black}{\frac{1}{\sqrt{a+b+2}}+\frac{1}{\sqrt{c+b+2}}+\frac{1}{\sqrt{a+c+2}}\ge1+\frac{1}{\sqrt{2(a+b+c-1)}}.}$

Published on 26 Mar 2026 - 8:02

List Question

Can't understand proof of fundamental theorem of symmetric polynomials

Schur $Q-$functions

Finding $\small{\max\limits_{ab+bc+ca=1}\dfrac{\sqrt{a+bc}+\sqrt{b+ca}+\sqrt{c+ab}}{\sqrt{3a+3b+3c+10}} }$

What's the name for this method of putting the roots of a polynomial in a system of equations?

Prove $\frac{a}{\sqrt{4a+3bc}}+\frac{b}{\sqrt{4b+3ca}}+\frac{c}{\sqrt{4c+3ab}}\le \frac{\sqrt{a+b+c+2}}{2}.$

Prove that $\frac{1}{\sqrt{4a+bc}}+\frac{1}{\sqrt{4b+ca}}+\frac{1}{\sqrt{4c+ab}}\le \sqrt{2(a+b+c)}.$

inverting the first three elementary symmetric polynomials

Minimizing $ \sum\limits_{cyc}\frac{\sqrt{5a+8bc}}{8a+5bc}$ with $ \sum\limits_{cyc}ab=1$

Prove $\sqrt{a+b-2ab}+\sqrt{c+b-2bc}+\sqrt{a+c-2ca}\ge 2\sqrt{a+b+c-1}.$

Prove $\sqrt{\frac{a+b}{c+ab}}+\sqrt{\frac{c+b}{a+cb}}+\sqrt{\frac{a+c}{b+ac}}\ge 3,$ if $ab+bc+ca=3.$

$\sum \frac{a^2+b^2}{c^2}-\frac{7}{2} \geq \sqrt[3]{\prod \left(\frac{a}{b+c}+\frac{1}{3}\right)}$ for a,b,c real

Prove that tan($Z$) = $\frac{e_1t - e_3t^3 + e_5t^5 - \cdots}{1 - e_2t^2 + e_4t^4 - \cdots}$

What are the generators of polynomials symmetric under a subgroup of the permutation group

How to prove $ a+b+c+\sqrt{bc}+\sqrt{ca}+\sqrt{ab}\ge 6$?

Prove $\color{black}{\frac{1}{\sqrt{a+b+2}}+\frac{1}{\sqrt{c+b+2}}+\frac{1}{\sqrt{a+c+2}}\ge1+\frac{1}{\sqrt{2(a+b+c-1)}}.}$

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