List questions from symmetric-polynomials

Published on 25 Jun 2018 - 15:32

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If $α, β, γ$ are roots of $x^3 - x -1 = 0$, then find the value of $\frac{1+α}{1-α} + \frac{1+β}{1-β} + \frac{1+γ}{1-γ}$.

Published on 25 Mar 2026 - 3:04

119

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Proving $\Big(a+\frac{1}{b}\Big)^2 + \Big(b+\frac{1}{c}\Big)^2 + \Big(c+\frac{1}{a}\Big)^2 \geq 3(a+b+c+1)$

Published on 28 Jun 2018 - 16:18

152

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Prove $\sum\limits_{cyc} \frac{1- x_{1}}{5\,{x_{1}}^{4}- 9\,{x_{1}}^{2}- 450}\geq 0$

Published on 25 Mar 2026 - 6:13

80

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solution to equations having 4 variables

Published on 10 Jul 2018 - 13:59

61

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Solve set of nonlinear equation

Published on 11 Jul 2018 - 5:04

170

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How to find a symmetric polynomial's non-symmetric equivalent?

Published on 23 Feb 2026 - 10:47

74

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Can we conclude that two of the variables must be $0$?

Published on 15 Jul 2018 - 12:53

525

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prove this inequality $(x+y-z)(y+z-x)(x+z-y)(x+y+z)^3\le27 (xyz)^2$

Published on 16 Jul 2018 - 13:40

260

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$ \frac {3 x y z}{(x+y) (y+z) (z+x)} + \sum\limits_{cycl}^{} \left(\frac {x+y}{x+y+ 2 z}\right)^2 \ge \frac {9}{8}.$

Published on 25 Mar 2026 - 4:43

412

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Prove that $a^4+b^4+1\ge a+b$.

Published on 20 Jul 2018 - 20:28

68

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Existence of a solution for a symmetric homogeneous polynomial equation

Published on 23 Jul 2018 - 19:29

71

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Strengthening an inequality of exponential series

Published on 29 Jul 2018 - 18:51

44

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Real single solution of an algebraic nonlinear system

Published on 29 Jul 2018 - 21:57

116

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Is $|abc|+|bcd|+|abd|+|acd|$ a norm on $\mathbb{R}^4$?

Published on 30 Jul 2018 - 20:27

List Question

Prove that inequality

If $α, β, γ$ are roots of $x^3 - x -1 = 0$, then find the value of $\frac{1+α}{1-α} + \frac{1+β}{1-β} + \frac{1+γ}{1-γ}$.

Proving $\Big(a+\frac{1}{b}\Big)^2 + \Big(b+\frac{1}{c}\Big)^2 + \Big(c+\frac{1}{a}\Big)^2 \geq 3(a+b+c+1)$

Prove $\sum\limits_{cyc} \frac{1- x_{1}}{5\,{x_{1}}^{4}- 9\,{x_{1}}^{2}- 450}\geq 0$

solution to equations having 4 variables

Solve set of nonlinear equation

How to find a symmetric polynomial's non-symmetric equivalent?

Can we conclude that two of the variables must be $0$?

prove this inequality $(x+y-z)(y+z-x)(x+z-y)(x+y+z)^3\le27 (xyz)^2$

$ \frac {3 x y z}{(x+y) (y+z) (z+x)} + \sum\limits_{cycl}^{} \left(\frac {x+y}{x+y+ 2 z}\right)^2 \ge \frac {9}{8}.$

Prove that $a^4+b^4+1\ge a+b$.

Existence of a solution for a symmetric homogeneous polynomial equation

Strengthening an inequality of exponential series

Real single solution of an algebraic nonlinear system

Is $|abc|+|bcd|+|abd|+|acd|$ a norm on $\mathbb{R}^4$?

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