List questions from cauchy-schwarz-inequality

Published on 15 May 2026 - 6:26

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$a^2b^2+a^2c^2+b^2c^2\leq 3$

Published on 16 Apr 2026 - 6:54

98

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Prove that $\;\sum_{i=1}^n \frac{p_i}{p_{i+1}+p_{i+2}} \ge \frac{n}{2}$ using Jensen's inequality

Published on 10 May 2026 - 23:39

1.5k

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Show that the Frobenius norm is compatible with the Euclidean norm

Published on 25 Mar 2026 - 17:39

254

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$x,y,z > 0$, prove that $ 3xyz + x^{3}+ y^{3} + z^{3} \ge 2 \left[ (xy)^{3/2} + (yz)^{3/2} + (xz)^{3/2} \right] $

Published on 27 Mar 2026 - 19:10

112

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Prove that $\sum _{cyc}\sqrt{1-\frac{\left(a+b\right)^2}{4}}\ge \sqrt{6}$

Published on 15 Apr 2026 - 21:11

34

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Cauchy Schwarz Inequality

Published on 14 Apr 2026 - 9:38

86

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Prove that$\frac{1}{(x+1)^2+y^2+1}+\frac{1}{(y+1)^2+z^2+1}+\frac{1}{(z+1)^2+x^2+1}\le\frac{1}{2}$

Published on 27 Mar 2026 - 21:03

97

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Find scalars $a_{ir}$ such that $\| a_{ir} x_{ir} \|^2 \geq \prod_{j \neq i} | \langle a_{js} x_{js}, a_{jt} x_{jt} \rangle |$ for all $s, t$

Published on 14 Apr 2026 - 18:56

204

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Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$

Published on 27 Mar 2026 - 21:03

181

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Proving $\sum_{cyc} \sqrt{a^2+ab+b^2}\geq\sqrt 3$ when $a+b+c=3$

Published on 05 May 2026 - 6:56

53

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three variable inequality $\sum \frac{x}{1+2x+xy}$

Published on 14 Apr 2026 - 7:47

129

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A lower bound for $\sum\limits_\text{cyc} \frac{x}{\sqrt{x^2+y^2}}$

Published on 14 Apr 2026 - 4:21

89

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For $ab+bc+ca=3$, when does $\prod_\text{cyc}(a^8+1)(a^4+1)=\prod_\text{cyc}(a^2+1)^2$?

Published on 15 Apr 2026 - 22:43

72

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Prove that $\sum_\text{cyc} \frac{ab}{ab+b^2+ca}\le 1$

Published on 16 Apr 2026 - 4:50

List Question

An elegant but difficult inequality.

$a^2b^2+a^2c^2+b^2c^2\leq 3$

Prove that $\;\sum_{i=1}^n \frac{p_i}{p_{i+1}+p_{i+2}} \ge \frac{n}{2}$ using Jensen's inequality

Show that the Frobenius norm is compatible with the Euclidean norm

$x,y,z > 0$, prove that $ 3xyz + x^{3}+ y^{3} + z^{3} \ge 2 \left[ (xy)^{3/2} + (yz)^{3/2} + (xz)^{3/2} \right] $

Prove that $\sum _{cyc}\sqrt{1-\frac{\left(a+b\right)^2}{4}}\ge \sqrt{6}$

Cauchy Schwarz Inequality

Prove that$\frac{1}{(x+1)^2+y^2+1}+\frac{1}{(y+1)^2+z^2+1}+\frac{1}{(z+1)^2+x^2+1}\le\frac{1}{2}$

Find scalars $a_{ir}$ such that $\| a_{ir} x_{ir} \|^2 \geq \prod_{j \neq i} | \langle a_{js} x_{js}, a_{jt} x_{jt} \rangle |$ for all $s, t$

Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$

Proving $\sum_{cyc} \sqrt{a^2+ab+b^2}\geq\sqrt 3$ when $a+b+c=3$

three variable inequality $\sum \frac{x}{1+2x+xy}$

A lower bound for $\sum\limits_\text{cyc} \frac{x}{\sqrt{x^2+y^2}}$

For $ab+bc+ca=3$, when does $\prod_\text{cyc}(a^8+1)(a^4+1)=\prod_\text{cyc}(a^2+1)^2$?

Prove that $\sum_\text{cyc} \frac{ab}{ab+b^2+ca}\le 1$

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