List questions from sum-of-squares-method

Published on 04 Oct 2020 - 13:30

72

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Explanation to an unmotivated step in an inequality.

Published on 05 Oct 2020 - 12:11

109

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Prove $\frac{4}{a^2 + 2b^2 + 3c^2 + 10} \le \frac{5a + 3b + c + 7d}{16(a+b+c+d)}$ for positive reals $abcd=1$

Published on 09 Oct 2020 - 3:31

193

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Expressing a polynomial as a sum of squares in Maple

Published on 10 Oct 2020 - 6:23

251

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Sum of two squares question

Published on 14 Oct 2020 - 14:45

82

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How to formulate Augmented Langrangian as an objective function to SOS problem?

Published on 15 Oct 2020 - 10:43

131

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For $a,b,c>0$ proving $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geqslant a + b + c + \frac{4(a - b)^2}{a + b + c}$

Published on 18 Oct 2020 - 2:56

151

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Proving a cyclic inequality

Published on 25 Mar 2026 - 23:17

145

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Prove $5\Big(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\Big)\geq \frac{a^2+b^2+c^2}{ab+bc+ca}+10.$

Published on 26 Mar 2026 - 1:23

117

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Prove $3\left(9-5\sqrt{3}\right) \sum \frac{1}{a} \geqslant \sum a^2+\frac32\cdot\frac{\left[(\sqrt3-2)(ab+bc+ca)+abc\right]^2}{abc}$

Published on 26 Mar 2026 - 19:20

118

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$\frac{b^2-a^2}{c+a} + \frac{c^2-b^2}{a+b} + \frac{a^2-c^2}{b+c} \ge 0$ Proof

Published on 25 Mar 2026 - 23:24

178

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prove thatt $\sum_{cyc} \frac{1}{{(x+y)}^2}\ge 9/4$

Published on 01 Nov 2020 - 8:53

101

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Inequality $\frac{xy+z}{x+yz}+\frac{yz+x}{y+zx}+\frac{zx+y}{z+xy}-\frac{x+y+z}{3}\leq 1$

Published on 18 Nov 2020 - 8:46

36

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If the real zeroes of real polynomial $p(x,y)$ are disjoint points and curves, is $p(x,y)$ a positive sum of squares?

Published on 25 Mar 2026 - 14:25

270

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Prove the polynomial $x^4+4 x^3+4 x^2-4 x+3$ is positive

Published on 11 Jan 2021 - 10:04

List Question

A cyclic inequality of degree 10

Explanation to an unmotivated step in an inequality.

Prove $\frac{4}{a^2 + 2b^2 + 3c^2 + 10} \le \frac{5a + 3b + c + 7d}{16(a+b+c+d)}$ for positive reals $abcd=1$

Expressing a polynomial as a sum of squares in Maple

Sum of two squares question

How to formulate Augmented Langrangian as an objective function to SOS problem?

For $a,b,c>0$ proving $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geqslant a + b + c + \frac{4(a - b)^2}{a + b + c}$

Proving a cyclic inequality

Prove $5\Big(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\Big)\geq \frac{a^2+b^2+c^2}{ab+bc+ca}+10.$

Prove $3\left(9-5\sqrt{3}\right) \sum \frac{1}{a} \geqslant \sum a^2+\frac32\cdot\frac{\left[(\sqrt3-2)(ab+bc+ca)+abc\right]^2}{abc}$

$\frac{b^2-a^2}{c+a} + \frac{c^2-b^2}{a+b} + \frac{a^2-c^2}{b+c} \ge 0$ Proof

prove thatt $\sum_{cyc} \frac{1}{{(x+y)}^2}\ge 9/4$

Inequality $\frac{xy+z}{x+yz}+\frac{yz+x}{y+zx}+\frac{zx+y}{z+xy}-\frac{x+y+z}{3}\leq 1$

If the real zeroes of real polynomial $p(x,y)$ are disjoint points and curves, is $p(x,y)$ a positive sum of squares?

Prove the polynomial $x^4+4 x^3+4 x^2-4 x+3$ is positive

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