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

Published on 04 Mar 2018 - 15:29

270

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Symmetric Olympiad inequality

Published on 21 Mar 2026 - 23:50

157

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Is there a direct proof of the inequality $cyclic \sum\frac {a^2+1}{b+c}\ge 3$

Published on 11 Mar 2018 - 17:10

1.3k

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Find the smallest value of positive constant $m$ such that curve will never lie below $x$-axis?

Published on 14 Mar 2018 - 21:14

534

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Inequality $\frac{a}{\sqrt{bc}}\cdot\frac1{a+1}+\frac{b}{\sqrt{ca}}\cdot\frac1{b+1}+\frac{c}{\sqrt{ab}}\cdot\frac1{c+1}\leqslant\sqrt2.$

Published on 25 Mar 2026 - 3:04

77

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About QM power inequality.

Published on 27 Mar 2018 - 9:45

112

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Let $a> 0, b> 0$. Prove that: $\frac{{{a}^{2}}}{b}+\frac{{{b}^{2}}}{a}+7\left( a+b \right)\ge 8\sqrt{2\left( {{a}^{2}}+{{b}^{2}} \right)}$

Published on 25 Mar 2026 - 4:42

145

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Minimum of $\frac{x}{\sqrt{1-x^2}}+\frac{y}{\sqrt{1-y^2}}+\frac{z}{\sqrt{1-z^2}}$

Published on 01 Apr 2018 - 7:45

253

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When $xyz=1$ why is $x+y+z\geq3$? ($x,y,z>0$)

Published on 23 Mar 2026 - 4:24

530

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Prove this inequality $\sum_{cyc}\sqrt[4]{\frac{a}{b+c}}\ge \sqrt[4]{16+\frac{196abc}{(a+b)(b+c)(c+a)}}$

Published on 04 Apr 2018 - 11:39

233

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Interesting 3 Variable Inequality for Real Numbers

Published on 05 Apr 2018 - 18:37

625

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Find the maximum value a product

Published on 07 Apr 2018 - 21:07

115

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Comparing $\left({\frac{2^{10}}{11}}\right)^{11}$ and $\binom{10}1^2\cdot\binom{10}2^2\cdot\binom{10}3^2\cdot\binom{10}4^2\cdot\binom{10}5$

Published on 12 Apr 2018 - 5:36

71

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How to properly apply AM-GM inequality?

Published on 20 Apr 2018 - 16:50

98

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Subtle Carefulness in use of AM-GM inequality

Published on 21 Apr 2018 - 15:24

List Question

why is Arithmetic mean minimum when all terms are equal

Symmetric Olympiad inequality

Is there a direct proof of the inequality $cyclic \sum\frac {a^2+1}{b+c}\ge 3$

Find the smallest value of positive constant $m$ such that curve will never lie below $x$-axis?

Inequality $\frac{a}{\sqrt{bc}}\cdot\frac1{a+1}+\frac{b}{\sqrt{ca}}\cdot\frac1{b+1}+\frac{c}{\sqrt{ab}}\cdot\frac1{c+1}\leqslant\sqrt2.$

About QM power inequality.

Let $a> 0, b> 0$. Prove that: $\frac{{{a}^{2}}}{b}+\frac{{{b}^{2}}}{a}+7\left( a+b \right)\ge 8\sqrt{2\left( {{a}^{2}}+{{b}^{2}} \right)}$

Minimum of $\frac{x}{\sqrt{1-x^2}}+\frac{y}{\sqrt{1-y^2}}+\frac{z}{\sqrt{1-z^2}}$

When $xyz=1$ why is $x+y+z\geq3$? ($x,y,z>0$)

Prove this inequality $\sum_{cyc}\sqrt[4]{\frac{a}{b+c}}\ge \sqrt[4]{16+\frac{196abc}{(a+b)(b+c)(c+a)}}$

Interesting 3 Variable Inequality for Real Numbers

Find the maximum value a product

Comparing $\left({\frac{2^{10}}{11}}\right)^{11}$ and $\binom{10}1^2\cdot\binom{10}2^2\cdot\binom{10}3^2\cdot\binom{10}4^2\cdot\binom{10}5$

How to properly apply AM-GM inequality?

Subtle Carefulness in use of AM-GM inequality

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