List questions from sum-of-squares-method

Published on 20 Mar 2026 - 7:08

156

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Prove the next cyclic inequality

Published on 19 Mar 2026 - 21:51

221

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I have a inequality, I don't know where to start

Published on 20 Mar 2026 - 5:22

915

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How can one prove that this polynomial is non-negative?

Published on 22 Mar 2026 - 22:52

929

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How to prove expression greater than 0

Published on 23 Mar 2026 - 10:23

114

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Homogeneous fourth degree inequality : $\sum x_i^2x_j^2 +6x_1x_2x_3x_4 \geq\sum x_ix_jx_k^2$

Published on 23 Mar 2026 - 10:25

137

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Find minimum value of $\sum \frac {\sqrt a}{\sqrt b +\sqrt c-\sqrt a}$

Published on 21 Mar 2026 - 18:13

324

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Triangle inequality $\frac{ab}{a^{2}+ b^{2}}+ \frac{bc}{b^{2}+ c^{2}}+ \frac{ca}{c^{2}+ a^{2}}\geq \frac{1}{2}+ \frac{2r}{R}$

Published on 20 Mar 2026 - 6:55

119

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Prove this stronger inequality

Published on 23 Mar 2026 - 10:50

425

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Express $x^4 + y^4 + x^2 + y^2$ as sum of squares of three polynomials in $x,y$

Published on 22 Mar 2026 - 10:40

91

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For $a>0,b>0,c>0$, prove $\frac{a(a^2+bc)}{b+c}+\frac{b(b^2+ca)}{bc+a}+\frac{c(c^2+ab)}{a+b}\geq ab+bc+ca$

Published on 23 Mar 2026 - 3:25

109

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If $a_i>0$ and $\sum_{i=1}^n a_i = 1$, then $\sum_{i=1}^n \frac{1}{a_i} \geq n^2$?

Published on 22 Mar 2026 - 19:31

120

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Question from a Moscow summer camp

Published on 25 Mar 2026 - 6:10

482

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Prove that $3\left(\frac{x}{y} + \frac{y}{z} + \frac{z}{x}\right) \geq 2(x + y + z)\left (\frac{1}{y + z} + \frac{1}{x + z} + \frac{1}{x + y}\right)$

Published on 25 Mar 2026 - 6:13

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

List Question

An algebraic inequality involving $\sum_{cyc} \frac1{(a+2b+3c)^2}$

Prove the next cyclic inequality

I have a inequality, I don't know where to start

How can one prove that this polynomial is non-negative?

How to prove expression greater than 0

Homogeneous fourth degree inequality : $\sum x_i^2x_j^2 +6x_1x_2x_3x_4 \geq\sum x_ix_jx_k^2$

Find minimum value of $\sum \frac {\sqrt a}{\sqrt b +\sqrt c-\sqrt a}$

Triangle inequality $\frac{ab}{a^{2}+ b^{2}}+ \frac{bc}{b^{2}+ c^{2}}+ \frac{ca}{c^{2}+ a^{2}}\geq \frac{1}{2}+ \frac{2r}{R}$

Prove this stronger inequality

Express $x^4 + y^4 + x^2 + y^2$ as sum of squares of three polynomials in $x,y$

For $a>0,b>0,c>0$, prove $\frac{a(a^2+bc)}{b+c}+\frac{b(b^2+ca)}{bc+a}+\frac{c(c^2+ab)}{a+b}\geq ab+bc+ca$

If $a_i>0$ and $\sum_{i=1}^n a_i = 1$, then $\sum_{i=1}^n \frac{1}{a_i} \geq n^2$?

Question from a Moscow summer camp

Prove that $3\left(\frac{x}{y} + \frac{y}{z} + \frac{z}{x}\right) \geq 2(x + y + z)\left (\frac{1}{y + z} + \frac{1}{x + z} + \frac{1}{x + y}\right)$

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

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