List questions from a-m-g-m-inequality

Published on 23 Mar 2026 - 1:04

445

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Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Published on 25 Mar 2026 - 19:02

442

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Which is bigger, $ \log_{1000} 1001$ or $\log_{999} 1000 $?

Published on 22 Mar 2026 - 18:26

79

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Proving at least one number $\le 1/4$

Published on 25 Mar 2026 - 9:09

221

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Proving that $\cosh(x)\cosh(y) \geq \sqrt{x^2 + y^2}$

Published on 25 Mar 2026 - 6:12

96

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A geometric inequality for a triangle ABC

Published on 25 Mar 2026 - 16:06

110

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Problem inequality

Published on 25 Mar 2026 - 12:45

149

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Quadratic inequality where $x\in\mathbb{R}$

Published on 22 Jun 2018 - 20:06

90

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Can inequalities be proven by taking all variables to be equal?

Published on 25 Mar 2026 - 1:16

228

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Prove that if $x^3 + y^3 \geq a^3$ then $x^2 + y^2 > a^2$

Published on 26 Jun 2018 - 19:44

70

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Is this a typo?

Published on 27 Jun 2018 - 17:13

120

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Proving $\Big(a+\frac{1}{b}\Big)^2 + \Big(b+\frac{1}{c}\Big)^2 + \Big(c+\frac{1}{a}\Big)^2 \geq 3(a+b+c+1)$

Published on 25 Mar 2026 - 12:49

63

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Inequalities on sum of a finite sequence

Published on 29 Jun 2018 - 15:38

160

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Problem in Arithmetic Mean - Geometric Mean inequality

Published on 29 Jun 2018 - 23:21

505

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Minimal area of a right triangle with inradius $1$

Published on 25 Mar 2026 - 16:01

List Question

Show that $a^2(a+b)^3+b^2(b+c)^3+c^2(c+a)^3\geq{\frac{8abc(a+b+c)^2}{3}}$ holds for $a,b,c>0$

Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Which is bigger, $ \log_{1000} 1001$ or $\log_{999} 1000 $?

Proving at least one number $\le 1/4$

Proving that $\cosh(x)\cosh(y) \geq \sqrt{x^2 + y^2}$

A geometric inequality for a triangle ABC

Problem inequality

Quadratic inequality where $x\in\mathbb{R}$

Can inequalities be proven by taking all variables to be equal?

Prove that if $x^3 + y^3 \geq a^3$ then $x^2 + y^2 > a^2$

Is this a typo?

Proving $\Big(a+\frac{1}{b}\Big)^2 + \Big(b+\frac{1}{c}\Big)^2 + \Big(c+\frac{1}{a}\Big)^2 \geq 3(a+b+c+1)$

Inequalities on sum of a finite sequence

Problem in Arithmetic Mean - Geometric Mean inequality

Minimal area of a right triangle with inradius $1$

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