List questions from symmetric-polynomials

Published on 23 Sep 2018 - 10:15

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$x^2 y = 1$, $y^2 z = 128$, $z^2 x = 32$

Published on 25 Mar 2026 - 6:05

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If $\sum\limits_{\text{cyc}}x=\frac\pi2$, then $2\sqrt{\sum\limits_{\text{cyc}}\tan x}\le\sum\limits_{\text{cyc}}\frac{\sqrt{\tan x}}{\cos x}$

Published on 25 Sep 2018 - 7:19

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How to prove inequality $(a^2+b^2+c^2)^3\ge6(a^3+b^3+c^3)^2$ when $a+b+c=0$?

Published on 25 Sep 2018 - 14:08

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If $a^2+b^2 \gt a+b$ and $a,b \gt 0$ Prove that $a^3+b^3 \gt a^2+b^2$

Published on 28 Sep 2018 - 6:37

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When is the quotient of an algebra by a polynomial algebra a free module?

Published on 25 Mar 2026 - 3:21

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Prove $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}} \le \frac{3}{2}$

Published on 05 Oct 2018 - 18:29

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How to prove $f(x)=x^4$ is concave up by definition?

Published on 10 Oct 2018 - 14:31

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If $\alpha$ and $\beta$ are roots of $(x^2)-(4x)-1=0$, find $\sqrt[3]{\alpha}+ \sqrt[3]{\beta}$

Published on 25 Mar 2026 - 9:10

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Show that $\frac {1}{3+x^2+y^2} + \frac {1}{3+y^2+z^2} +\frac{1} {3+x^2+z^2}\leq \frac {3}{5} . $

Published on 25 Mar 2026 - 4:43

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Prove that if $x_1 + x_2 + ... + x_n = n$, then $x_1^k + x_2^k + ... + x_n^k \ge n$

Published on 25 Mar 2026 - 1:40

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Find maximum value

Published on 18 Oct 2018 - 4:13

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Higher Algebra by Hall & Knight: Chapter 1, Art 16, Example 3

Published on 22 Oct 2018 - 14:59

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Solve this question

Published on 23 Oct 2018 - 18:04

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Understanding an algebra isomorphism resulting from the fundamental theorem of symmetric polynomials

Published on 28 Oct 2018 - 11:34

List Question

Cyclic vs Symmetric Polynomials

$x^2 y = 1$, $y^2 z = 128$, $z^2 x = 32$

If $\sum\limits_{\text{cyc}}x=\frac\pi2$, then $2\sqrt{\sum\limits_{\text{cyc}}\tan x}\le\sum\limits_{\text{cyc}}\frac{\sqrt{\tan x}}{\cos x}$

How to prove inequality $(a^2+b^2+c^2)^3\ge6(a^3+b^3+c^3)^2$ when $a+b+c=0$?

If $a^2+b^2 \gt a+b$ and $a,b \gt 0$ Prove that $a^3+b^3 \gt a^2+b^2$

When is the quotient of an algebra by a polynomial algebra a free module?

Prove $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}} \le \frac{3}{2}$

How to prove $f(x)=x^4$ is concave up by definition?

If $\alpha$ and $\beta$ are roots of $(x^2)-(4x)-1=0$, find $\sqrt[3]{\alpha}+ \sqrt[3]{\beta}$

Show that $\frac {1}{3+x^2+y^2} + \frac {1}{3+y^2+z^2} +\frac{1} {3+x^2+z^2}\leq \frac {3}{5} . $

Prove that if $x_1 + x_2 + ... + x_n = n$, then $x_1^k + x_2^k + ... + x_n^k \ge n$

Find maximum value

Higher Algebra by Hall & Knight: Chapter 1, Art 16, Example 3

Solve this question

Understanding an algebra isomorphism resulting from the fundamental theorem of symmetric polynomials

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