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

Published on 26 Mar 2026 - 8:14

184

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Prove a trigonometric inequality

Published on 08 Jan 2020 - 20:58

59

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Show that the inequality $\frac{s}{t} + \frac{t}{r} + \frac{r}{s} >= 3$, assuming s,t,r >0.

Published on 08 Jan 2020 - 21:09

317

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Proving an inequality containing 3 variables

Published on 09 Jan 2020 - 22:29

111

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Proving an inequality involving fractions and square roots holds

Published on 13 Jan 2020 - 2:11

73

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How to prove that $\frac1a+\frac3b+2(a+\sqrt{b^2+8})>11$

Published on 13 Jan 2020 - 17:36

45

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Not sure what to do after trying to simplify the inequality and getting nowhere?

Published on 14 Jan 2020 - 1:38

62

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How can the AM-GM inequality be used in this case if the given variables are real numbers?

Published on 15 Jan 2020 - 4:14

41

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Not really sure how to proceed further with this inequality

Published on 27 Mar 2026 - 9:12

150

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How to prove the harmonic-geometric mean inequality by solving an optimization?

Published on 25 Mar 2026 - 6:02

97

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Prove that $\left|\frac{x^3y^3}{9x^4+y^4}\right| \le \frac{x^2+y^2}{6}$

Published on 17 Jan 2020 - 5:41

118

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I$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2} + c^{2} + 1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 \implies ab + ac + bc \le 3$

Published on 19 Jan 2020 - 13:02

180

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Prove $\sqrt{a^2+4}+\sqrt{b^2+4}\leq\frac{\sqrt{2}}{4}(a+b)^2$ with $\frac1a+\frac1b=1$.

Published on 24 Jan 2020 - 17:15

265

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A Question about a proof of the AM-GM inequality

Published on 25 Jan 2020 - 8:35

136

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Minimum value of $p=3x+\frac{1}{15x}+5y+\frac{25}{y}+z+\frac{1}{36z},$ where $x,y,z\in \mathbb{R}^+$.

Published on 25 Jan 2020 - 14:55

List Question

Inequality Solution Correctness

Prove a trigonometric inequality

Show that the inequality $\frac{s}{t} + \frac{t}{r} + \frac{r}{s} >= 3$, assuming s,t,r >0.

Proving an inequality containing 3 variables

Proving an inequality involving fractions and square roots holds

How to prove that $\frac1a+\frac3b+2(a+\sqrt{b^2+8})>11$

Not sure what to do after trying to simplify the inequality and getting nowhere?

How can the AM-GM inequality be used in this case if the given variables are real numbers?

Not really sure how to proceed further with this inequality

How to prove the harmonic-geometric mean inequality by solving an optimization?

Prove that $\left|\frac{x^3y^3}{9x^4+y^4}\right| \le \frac{x^2+y^2}{6}$

I$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2} + c^{2} + 1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 \implies ab + ac + bc \le 3$

Prove $\sqrt{a^2+4}+\sqrt{b^2+4}\leq\frac{\sqrt{2}}{4}(a+b)^2$ with $\frac1a+\frac1b=1$.

A Question about a proof of the AM-GM inequality

Minimum value of $p=3x+\frac{1}{15x}+5y+\frac{25}{y}+z+\frac{1}{36z},$ where $x,y,z\in \mathbb{R}^+$.

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