Question

Choose the variables so that the weighted symmetric polynomial is minimal.

score 86 · Answer 1 · 2013-03-09 15:10:38

86

Views

Choose the variables so that the weighted symmetric polynomial is minimal.

Published on 09 Mar 2013 - 15:10

score 338 · Answer 2 · 2013-03-10 16:12:29

338

Views

Equal-variables problem in three variables

Published on 10 Mar 2013 - 16:12

score 3.5k · Answer 3 · 2026-03-26 14:20:53

3.5k

Views

How to prove this inequality? $ab+ac+ad+bc+bd+cd\le a+b+c+d+2abcd$

Published on 26 Mar 2026 - 14:20

score 185 · Answer 4 · 2026-03-26 17:51:47

185

Views

Help with inequality please

Published on 26 Mar 2026 - 17:51

score 112 · Answer 5 · 2026-03-25 09:26:11

112

Views

Die Relationen, welche zwischen den elementaren symmetrischen Functionen bestehen - Translation?

Published on 25 Mar 2026 - 9:26

score 4.9k · Answer 6 · 2013-03-20 03:04:22

4.9k

Views

Proofs of The Fundamental Theorem of Symmetric Polynomials

Published on 20 Mar 2013 - 3:04

score 551 · Answer 7 · 2026-03-26 11:18:17

551

Views

Understanding the Fundamental Theorem of Symmetric Polynomials within the context of proving $\pi$ transcendental

Published on 26 Mar 2026 - 11:18

score 54 · Answer 8 · 2013-03-24 15:35:50

54

Views

$p(x)$ be a polynomial over $\mathbb{Z}$. If $P(a)=P(b)=P(c)=-1$ with integers $a,b,c$.Then $P(x)$ has no integral roots

Published on 24 Mar 2013 - 15:35

score 1.8k · Answer 9 · 2026-03-25 21:54:10

1.8k

Views

If $a^2 + b^2 + c^2 = 1$, what is the the minimum value of $\frac {ab}{c} + \frac {bc}{a} + \frac {ca}{b}$?

Published on 25 Mar 2026 - 21:54

score 144 · Answer 10 · 2020-08-02 20:38:50

144

Views

Orthocenter, Circumcenter, and Circumradius

Published on 02 Aug 2020 - 20:38

score 257 · Answer 11 · 2026-03-25 15:47:10

257

Views

Proving $(1+a^2)(1+b^2)(1+c^2)\geq8 $

Published on 25 Mar 2026 - 15:47

score 186 · Answer 12 · 2026-03-29 19:14:26

186

Views

Prove $( xy+2x+2y+1 ) ^{2} ( x+y+2 ) ^{2}\geqslant \frac14 [xy(x+y)+2(x^2+y^2)-18xy+5(x+y)+2 ] ^{2}+144xy ( {x}^{2}+{y}^{2}+2) $

Published on 29 Mar 2026 - 19:14

score 118 · Answer 13 · 2020-08-06 21:34:22

118

Views

Show that $xy$ cannot be written as a polynomial in $x+y$ and $x^2+y^2$

Published on 06 Aug 2020 - 21:34

score 1.5k · Answer 14 · 2026-03-27 12:28:55

1.5k

Views

Let $x_1,x_2,x_3,x_4$ denote the four roots of the equation $x^4 + kx^2 + 90x - 2009 = 0$. If $x_1x_2 = 49$, then find the value of $k$.

Published on 27 Mar 2026 - 12:28

score 148 · Answer 15 · 2026-03-25 19:10:06

148

Views

Proving $\sum_{cyc}\sqrt{a^4+a^2b^2+b^4}\geq \sum_{cyc} a\sqrt{2a^2+bc}$ for non-negative $a$, $b$, $c$

Published on 25 Mar 2026 - 19:10

List Question

Choose the variables so that the weighted symmetric polynomial is minimal.

Equal-variables problem in three variables

How to prove this inequality? $ab+ac+ad+bc+bd+cd\le a+b+c+d+2abcd$

Help with inequality please

Die Relationen, welche zwischen den elementaren symmetrischen Functionen bestehen - Translation?

Proofs of The Fundamental Theorem of Symmetric Polynomials

Understanding the Fundamental Theorem of Symmetric Polynomials within the context of proving $\pi$ transcendental

$p(x)$ be a polynomial over $\mathbb{Z}$. If $P(a)=P(b)=P(c)=-1$ with integers $a,b,c$.Then $P(x)$ has no integral roots

If $a^2 + b^2 + c^2 = 1$, what is the the minimum value of $\frac {ab}{c} + \frac {bc}{a} + \frac {ca}{b}$?

Orthocenter, Circumcenter, and Circumradius

Proving $(1+a^2)(1+b^2)(1+c^2)\geq8 $

Prove $( xy+2x+2y+1 ) ^{2} ( x+y+2 ) ^{2}\geqslant \frac14 [xy(x+y)+2(x^2+y^2)-18xy+5(x+y)+2 ] ^{2}+144xy ( {x}^{2}+{y}^{2}+2) $

Show that $xy$ cannot be written as a polynomial in $x+y$ and $x^2+y^2$

Let $x_1,x_2,x_3,x_4$ denote the four roots of the equation $x^4 + kx^2 + 90x - 2009 = 0$. If $x_1x_2 = 49$, then find the value of $k$.

Proving $\sum_{cyc}\sqrt{a^4+a^2b^2+b^4}\geq \sum_{cyc} a\sqrt{2a^2+bc}$ for non-negative $a$, $b$, $c$

Trending Questions

Popular # Hahtags

Popular Questions