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

Published on 11 Aug 2017 - 12:23

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Isosceles triangle inscribed in an ellipse.

Published on 11 Aug 2017 - 20:27

63

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Prove $x^{y+1}z+y^{z+1}x+z^{x+1}y\geq x^2y^2z^2$

Published on 12 Aug 2017 - 5:14

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If $s=1+\frac 12+\frac 13+......+\frac 1n$,then show that $(n+s)^s \gt n^n(n+1)$.

Published on 13 Aug 2017 - 15:33

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If $p$ and $q$ vary such that $3p + 2q = 50$, find the maximum value of $10pq$

Published on 17 Aug 2017 - 6:48

389

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Wanted: Low-dimensional SOS certificate for the AM-GM inequality

Published on 26 Mar 2026 - 12:58

2.2k

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Find the maximum value of $a^2b^3$ where $a,b$ are positive real numbers satisfying $a+b=10$

Published on 19 Aug 2017 - 16:45

65

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Question based on inequality with $\sum_{i=1}^{n}x_{i}=1$

Published on 22 Aug 2017 - 9:02

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If a, b, c>0 show that $\frac{a^2}{b^2+bc}+\frac{b^2}{c^2+ac}+\frac{c^2}{a^2+ab} \ge \frac{3}{2}$

Published on 25 Mar 2026 - 20:22

146

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Prove this inequality $\sum _{cyc}a^3+4\left(\sum _{cyc}\frac{ab}{a^2+b^2}\right)\ge 9$

Published on 26 Mar 2026 - 9:58

287

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Is this true $n!\leq(\frac{5n+7}{12})^n,n∈N$?

Published on 24 Aug 2017 - 8:43

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Prove that $ \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \le \frac{1}{8}$

Published on 26 Mar 2026 - 12:37

344

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How prove this inequality $x^3y+y^3z+z^3x\ge xyz(x+y+z)$

Published on 25 Mar 2026 - 20:22

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A question regarding minimum value of...

Published on 28 Aug 2017 - 20:41

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Finding the minimum value of $a^2+b^2+c^2$

Published on 01 Sep 2017 - 11:20

List Question

Algebra (inequalities)

Isosceles triangle inscribed in an ellipse.

Prove $x^{y+1}z+y^{z+1}x+z^{x+1}y\geq x^2y^2z^2$

If $s=1+\frac 12+\frac 13+......+\frac 1n$,then show that $(n+s)^s \gt n^n(n+1)$.

If $p$ and $q$ vary such that $3p + 2q = 50$, find the maximum value of $10pq$

Wanted: Low-dimensional SOS certificate for the AM-GM inequality

Find the maximum value of $a^2b^3$ where $a,b$ are positive real numbers satisfying $a+b=10$

Question based on inequality with $\sum_{i=1}^{n}x_{i}=1$

If a, b, c>0 show that $\frac{a^2}{b^2+bc}+\frac{b^2}{c^2+ac}+\frac{c^2}{a^2+ab} \ge \frac{3}{2}$

Prove this inequality $\sum _{cyc}a^3+4\left(\sum _{cyc}\frac{ab}{a^2+b^2}\right)\ge 9$

Is this true $n!\leq(\frac{5n+7}{12})^n,n∈N$?

Prove that $ \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \le \frac{1}{8}$

How prove this inequality $x^3y+y^3z+z^3x\ge xyz(x+y+z)$

A question regarding minimum value of...

Finding the minimum value of $a^2+b^2+c^2$

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