List questions from cauchy-schwarz-inequality

Published on 11 May 2026 - 10:09

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Prove that $\frac{1}{\sqrt{a+b+2}}+\frac{1}{\sqrt{b+c+2}}+\frac{1}{\sqrt{c+d+2}}+\frac{1}{\sqrt{d+a+2}}\le 2$

Published on 25 Mar 2026 - 16:08

90

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Elementary proof for the inequality

Published on 10 May 2026 - 18:19

118

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Find minimum of $a^2+b^2+\frac{a^2b^2}{(a+b)^2}-\frac{2(a^2+ab+b^2)}{a+b}$

Published on 28 Mar 2026 - 3:27

134

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For $a,b,c \ge 0$ real numbers, prove $\frac{2}{(1+a)^2}+\frac{2}{(1+b)^2}+\frac{2}{(1+c)^2} \geq \frac{9}{3+ab+bc+ca}$

Published on 10 May 2026 - 22:57

321

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Search for maximum and minimum functions on the surface in 3D

Published on 15 Apr 2026 - 18:25

141

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Prove that if $a,b,c > 0$ and $a + b + c = 1$, we have: $\frac{a^2}{a^3 + 5} + \frac{b^2}{b^3 + 5} + \frac{c^2}{c^3 + 5} \leq \frac{1}{4}$

Published on 28 Mar 2026 - 3:28

300

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Expectation value of the Frobenius norm of a matrix

Published on 12 Apr 2026 - 21:17

90

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Inequality to find the condition for positive semi-definite

Published on 10 May 2026 - 19:20

82

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Year 12 Proving homework question

Published on 15 Apr 2026 - 13:29

66

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How is $\sqrt{E(X-Y)^2}$ a distance function?

Published on 16 Apr 2026 - 3:11

124

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Given positives $a, b, c$ such that $a + b + c = 3$, prove that $\sum_{cyc}\frac{1}{a^2 + 4b^2 + c^2} \le \frac{1}{2}$.

Published on 11 May 2026 - 3:17

112

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How should I solve these inequalities?

Published on 28 Mar 2026 - 3:26

98

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Prove that $(ay-bx)^2+(az-cx)^2\ge (bz-cy)^2$

Published on 17 Apr 2026 - 3:44

349

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Does the Cauchy-Schwarz integral inequality still hold for convergent improper integrals?

Published on 14 May 2026 - 20:53

List Question

Hard inequality problem (if $(a_2-a_1)^2 + (a_3-a_2)^2 + \ldots + (a_{2n}-a_{2n-1})^2 = 1$ ...)

Prove that $\frac{1}{\sqrt{a+b+2}}+\frac{1}{\sqrt{b+c+2}}+\frac{1}{\sqrt{c+d+2}}+\frac{1}{\sqrt{d+a+2}}\le 2$

Elementary proof for the inequality

Find minimum of $a^2+b^2+\frac{a^2b^2}{(a+b)^2}-\frac{2(a^2+ab+b^2)}{a+b}$

For $a,b,c \ge 0$ real numbers, prove $\frac{2}{(1+a)^2}+\frac{2}{(1+b)^2}+\frac{2}{(1+c)^2} \geq \frac{9}{3+ab+bc+ca}$

Search for maximum and minimum functions on the surface in 3D

Prove that if $a,b,c > 0$ and $a + b + c = 1$, we have: $\frac{a^2}{a^3 + 5} + \frac{b^2}{b^3 + 5} + \frac{c^2}{c^3 + 5} \leq \frac{1}{4}$

Expectation value of the Frobenius norm of a matrix

Inequality to find the condition for positive semi-definite

Year 12 Proving homework question

How is $\sqrt{E(X-Y)^2}$ a distance function?

Given positives $a, b, c$ such that $a + b + c = 3$, prove that $\sum_{cyc}\frac{1}{a^2 + 4b^2 + c^2} \le \frac{1}{2}$.

How should I solve these inequalities?

Prove that $(ay-bx)^2+(az-cx)^2\ge (bz-cy)^2$

Does the Cauchy-Schwarz integral inequality still hold for convergent improper integrals?

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