List questions from symmetric-polynomials

Published on 26 Mar 2026 - 9:41

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prove a polynomial identity..

Published on 25 Mar 2026 - 23:24

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Prove that $a^2+b^2+c^2+3\sqrt[3]{a^2b^2c^2} \geq 2(ab+bc+ca).$

Published on 21 Mar 2026 - 21:52

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Prove the inequality with simple concepts

Published on 09 Jan 2016 - 17:53

636

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Center of the group algebra of the symmetric group

Published on 15 Jan 2016 - 21:06

96

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Calculating $a_1^4+a_2^4+a_3^4$ of the roots of a polynomial

Published on 16 Jan 2016 - 15:41

152

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Elementary symmetric polynomial task with three variables

Published on 28 Jan 2016 - 9:39

131

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Symmetric Polynomial in roots is in $F[X]$

Published on 01 Feb 2016 - 17:28

551

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Efficient way to compute the symmetric reduction of special polynomials (specially for resolvents)

Published on 25 Mar 2026 - 14:46

1.7k

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Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$

Published on 19 Feb 2016 - 19:09

167

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if $A,B,C$ are real numbers such that ,${ A }^{ 2 }+{ B }^{ 2 }+{ C }^{ 2 } = 1 $ and $A+B+C = 0 $ find the maximum value of $(ABC )^2$

Published on 25 Feb 2016 - 15:58

663

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Factorize $(x^2+y^2+z^2)(x+y+z)(x+y-z)(y+z-x)(z+x-y)-8x^2y^2z^2$

Published on 26 Mar 2026 - 9:18

254

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Compute the trace of $\text{Sym}^2 \left(f \right)$ and that of $\text{Sym}^3 \left(f \right)$.

Published on 03 Mar 2016 - 6:06

1.9k

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Solving system of three quadratic equations

Published on 04 Mar 2016 - 20:49

562

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Is it possible to "depress" any term in a polynomial with a suitable substitution?

Published on 05 Mar 2016 - 5:11

List Question

Inequality exercise (olympiad)

prove a polynomial identity..

Prove that $a^2+b^2+c^2+3\sqrt[3]{a^2b^2c^2} \geq 2(ab+bc+ca).$

Prove the inequality with simple concepts

Center of the group algebra of the symmetric group

Calculating $a_1^4+a_2^4+a_3^4$ of the roots of a polynomial

Elementary symmetric polynomial task with three variables

Symmetric Polynomial in roots is in $F[X]$

Efficient way to compute the symmetric reduction of special polynomials (specially for resolvents)

Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$

if $A,B,C$ are real numbers such that ,${ A }^{ 2 }+{ B }^{ 2 }+{ C }^{ 2 } = 1 $ and $A+B+C = 0 $ find the maximum value of $(ABC )^2$

Factorize $(x^2+y^2+z^2)(x+y+z)(x+y-z)(y+z-x)(z+x-y)-8x^2y^2z^2$

Compute the trace of $\text{Sym}^2 \left(f \right)$ and that of $\text{Sym}^3 \left(f \right)$.

Solving system of three quadratic equations

Is it possible to "depress" any term in a polynomial with a suitable substitution?

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