List questions from cauchy-schwarz-inequality

Published on 25 Mar 2026 - 20:39

58

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A Problem Involving an Inequality

Published on 26 Mar 2026 - 3:05

101

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Prove the inequality, power.

Published on 25 Mar 2026 - 22:09

330

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If $abc=1$ so $\sum\limits_{cyc}\frac{7-6a}{2+a^2}\geq1$

Published on 26 Mar 2026 - 1:14

105

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Maximize $\frac{1}{\sqrt{2a^2+b^2}}+\frac{1}{\sqrt{2a^2+c^2}}+\frac{1}{\sqrt{2c^2+a^2}}$ under some condition on $(a,b,c)$

Published on 16 Mar 2017 - 14:08

146

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Maximize $P=\frac{1}{\sqrt{1+x^{2}}}+\frac{1}{\sqrt{1+y^{2}}}+\frac{1}{\sqrt{1+z^{2}}}$

Published on 26 Mar 2026 - 3:08

475

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AM-GM giving wrong result on applying to trigonometric functions

Published on 29 Mar 2026 - 9:10

219

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Maximize $P=\frac{\sqrt{a^2-1}}{a}+\frac{\sqrt{b^2-1}}{b}+\frac{\sqrt{c^2-1}}{c} $

Published on 25 Mar 2026 - 22:06

660

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If $x + y + z + w=5$ then the minimum value of $x^2 \cot (9°) + y^2 \cot (27°) + z^2 \cot (63°) + w^2 \cot (81°)$ is?

Published on 25 Mar 2017 - 17:05

121

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Prove this $1+2abcxyz \geq a^2x^2 + b^2y^2+c^2z^2$

Published on 29 Mar 2026 - 15:33

294

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Showing that $(x_2 - x_1)^2 + (y_2 - y_1)^2 \leq 8$, where $x^2 + y^2 \leq 1$

Published on 08 Apr 2017 - 19:08

3.2k

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Prove that $\frac{1}{a^3(b+c)} + \frac{1}{b^3(a+c)} + \frac{1}{c^3(a+b)} \geq \frac{3}{2} \text{ when } abc=1$

Published on 25 Mar 2026 - 22:05

84

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A name for this statistical approximation?

Published on 30 Jan 2023 - 1:50

313

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Prove $\frac{ab^2+2}{a+c} +\frac{bc^2+2}{b+a} +\frac{ca^2+2}{c+b} \geq \frac{9}{2}$ for $a,b,c\geq1$

Published on 30 Jan 2023 - 6:57

106

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Prove that $(ab+bc+ca)\left( \frac{a}{b(b+1)}+\frac{b}{c(c+1)}+\frac{c}{a(a+1)}\right)\ge \frac{3}{4}$

Published on 31 Jan 2023 - 12:04

List Question

Square root inequality cyclic

A Problem Involving an Inequality

Prove the inequality, power.

If $abc=1$ so $\sum\limits_{cyc}\frac{7-6a}{2+a^2}\geq1$

Maximize $\frac{1}{\sqrt{2a^2+b^2}}+\frac{1}{\sqrt{2a^2+c^2}}+\frac{1}{\sqrt{2c^2+a^2}}$ under some condition on $(a,b,c)$

Maximize $P=\frac{1}{\sqrt{1+x^{2}}}+\frac{1}{\sqrt{1+y^{2}}}+\frac{1}{\sqrt{1+z^{2}}}$

AM-GM giving wrong result on applying to trigonometric functions

Maximize $P=\frac{\sqrt{a^2-1}}{a}+\frac{\sqrt{b^2-1}}{b}+\frac{\sqrt{c^2-1}}{c} $

If $x + y + z + w=5$ then the minimum value of $x^2 \cot (9°) + y^2 \cot (27°) + z^2 \cot (63°) + w^2 \cot (81°)$ is?

Prove this $1+2abcxyz \geq a^2x^2 + b^2y^2+c^2z^2$

Showing that $(x_2 - x_1)^2 + (y_2 - y_1)^2 \leq 8$, where $x^2 + y^2 \leq 1$

Prove that $\frac{1}{a^3(b+c)} + \frac{1}{b^3(a+c)} + \frac{1}{c^3(a+b)} \geq \frac{3}{2} \text{ when } abc=1$

A name for this statistical approximation?

Prove $\frac{ab^2+2}{a+c} +\frac{bc^2+2}{b+a} +\frac{ca^2+2}{c+b} \geq \frac{9}{2}$ for $a,b,c\geq1$

Prove that $(ab+bc+ca)\left( \frac{a}{b(b+1)}+\frac{b}{c(c+1)}+\frac{c}{a(a+1)}\right)\ge \frac{3}{4}$

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