List questions from symmetric-polynomials

Published on 28 Dec 2019 - 17:00

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If $\alpha, \beta,\gamma$ be the roots of $2x^3+x^2+x+1=0$, show that..........?

Published on 30 Dec 2019 - 13:43

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How does symmetry help solve an equation?

Published on 23 Feb 2026 - 4:52

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The definition of $s_I$ in Milnor and Stasheff, Characteristic classes, page 188

Published on 26 Mar 2026 - 1:29

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Is $x_0^4+x_1^4+x_2^4+x_3^4-ax_0x_1x_2x_3$ irreducible for every $a \in \mathbb{C}$?

Published on 03 Jan 2020 - 18:41

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Solve this equations system: $x^{5} + y^{5} + z^{5} = 1, x + y + z = 1$

Published on 06 Jan 2020 - 17:03

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show this inequality with the sum $\sum_{i=1}^{n}x_{i}=n$

Published on 06 Jan 2020 - 23:51

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For real numbers $x>0, y>0, z>0$ and $x y z=1 .$ prove that $ x^{6}+y^{6}+z^{6} \geq x^{5}+y^{5}+z^{5} $

Published on 25 Mar 2026 - 9:43

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$\begin{cases} x+xy=3 \\ xy^2+xy^3=12 \end{cases}$

Published on 07 Jan 2020 - 17:06

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$\begin{cases} x^4+x^2y^2+y^4=21 \\ x^2+xy+y^2=3 \end{cases}$

Published on 07 Jan 2020 - 17:47

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Help proving this inequality

Published on 08 Jan 2020 - 6:29

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Help with inequality problem

Published on 25 Mar 2026 - 10:59

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Given $a, b, c > 0$ such that $a^2 + b^2 + c^2 + abc = 4$, prove that $\sum_{cyc}\frac{b}{\sqrt{(c^2 + 2)(a^2 + 2)}} \ge 1$.

Published on 26 Mar 2026 - 8:23

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Expansion of $ \left(\sum_{i=1}^n x_i\right)^m$

Published on 10 Jan 2020 - 22:07

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Given positives $x$ and $y$ such that $x^2 + y^2 = xy + 1$, prove that $\frac{x}{x^2 + y} + \frac{y}{y^2 + x} \le 1$.

Published on 13 Jan 2020 - 14:31

List Question

Finite Products of three terms in term of polynomials

If $\alpha, \beta,\gamma$ be the roots of $2x^3+x^2+x+1=0$, show that..........?

How does symmetry help solve an equation?

The definition of $s_I$ in Milnor and Stasheff, Characteristic classes, page 188

Is $x_0^4+x_1^4+x_2^4+x_3^4-ax_0x_1x_2x_3$ irreducible for every $a \in \mathbb{C}$?

Solve this equations system: $x^{5} + y^{5} + z^{5} = 1, x + y + z = 1$

show this inequality with the sum $\sum_{i=1}^{n}x_{i}=n$

For real numbers $x>0, y>0, z>0$ and $x y z=1 .$ prove that $ x^{6}+y^{6}+z^{6} \geq x^{5}+y^{5}+z^{5} $

$\begin{cases} x+xy=3 \\ xy^2+xy^3=12 \end{cases}$

$\begin{cases} x^4+x^2y^2+y^4=21 \\ x^2+xy+y^2=3 \end{cases}$

Help proving this inequality

Help with inequality problem

Given $a, b, c > 0$ such that $a^2 + b^2 + c^2 + abc = 4$, prove that $\sum_{cyc}\frac{b}{\sqrt{(c^2 + 2)(a^2 + 2)}} \ge 1$.

Expansion of $ \left(\sum_{i=1}^n x_i\right)^m$

Given positives $x$ and $y$ such that $x^2 + y^2 = xy + 1$, prove that $\frac{x}{x^2 + y} + \frac{y}{y^2 + x} \le 1$.

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