List questions from sum-of-squares-method

Published on 04 May 2026 - 8:40

168

Views

Prove the next cyclic inequality

Published on 07 May 2026 - 16:52

232

Views

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

Published on 07 May 2026 - 12:48

924

Views

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

Published on 03 May 2026 - 16:38

938

Views

How to prove expression greater than 0

Published on 02 May 2026 - 20:18

123

Views

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

Published on 04 May 2026 - 8:58

144

Views

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

Published on 01 May 2026 - 6:57

330

Views

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 01 May 2026 - 7:57

127

Views

Prove this stronger inequality

Published on 30 Apr 2026 - 19:51

437

Views

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

Published on 02 May 2026 - 23:50

97

Views

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 05 May 2026 - 17:15

114

Views

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 29 Apr 2026 - 12:51

124

Views

Question from a Moscow summer camp

Published on 23 Apr 2026 - 5:55

487

Views

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 29 Apr 2026 - 12:51

156

Views

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

Published on 27 Apr 2026 - 6:04

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

Trending Questions

Popular # Hahtags

Popular Questions