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

Published on 12 May 2021 - 14:24

159

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Find maximum volume of a box using AM-GM inequality

Published on 13 May 2021 - 12:59

85

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Minimum of $\left(\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\right)$ where $a,b,c$ are the roots of a polynomial

Published on 22 May 2021 - 14:27

146

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AM-GM Inequality Problem

Published on 24 May 2021 - 21:19

144

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Triangle inequality involving side lengths and circumradius

Published on 07 Jun 2021 - 6:12

269

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An inequality using column sums of inverse matrices

Published on 23 Jun 2021 - 15:47

120

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If a,b,c,d,e are positive reals then prove the following inequality

Published on 28 Jun 2021 - 5:24

135

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Given non-negative real numbers, $a, b, c$, show that $2a + 2ab + abc \leq 18$ when $a + b + c = 5$

Published on 30 Jun 2021 - 16:32

145

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Prove that $2a + 2ab + abc \leq 18$ when $a + b + c = 5$ where $a, b, c \in \mathbb{R}$ without calculus.

Published on 01 Jul 2021 - 6:10

69

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Find $\max( a_{1} a_{2} ... a_{m} )$ where $\sum_{i=1}^{m} a_{i} = 1976$

Published on 07 Jul 2021 - 9:00

240

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$\sqrt n < n!^\frac1n\ \forall \ n$

Published on 31 Mar 2026 - 17:52

1.5k

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Prove that $\frac{\ 1}{a^2+b^2+ab}+\frac{\ 1}{b^2+c^2+bc}+\ \frac{\ 1}{c^2+a^2+ca}\ge\ \ \frac{\ 9}{\left(a+b+c\right)^2}$.

Published on 27 Mar 2026 - 4:58

76

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Chrystal's proof of the arithmetic-mean-geometric-mean inequality

Published on 14 Jul 2021 - 19:05

321

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Why AM-GM method can't be used to calculate the minimum value of $3\sin^2x+27\csc^2x$?

Published on 15 Jul 2021 - 13:39

99

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Find a good approximation of $r(x)$ for a proof

Published on 15 Jul 2021 - 15:09

List Question

Sum of certain products under constant sum

Find maximum volume of a box using AM-GM inequality

Minimum of $\left(\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\right)$ where $a,b,c$ are the roots of a polynomial

AM-GM Inequality Problem

Triangle inequality involving side lengths and circumradius

An inequality using column sums of inverse matrices

If a,b,c,d,e are positive reals then prove the following inequality

Given non-negative real numbers, $a, b, c$, show that $2a + 2ab + abc \leq 18$ when $a + b + c = 5$

Prove that $2a + 2ab + abc \leq 18$ when $a + b + c = 5$ where $a, b, c \in \mathbb{R}$ without calculus.

Find $\max( a_{1} a_{2} ... a_{m} )$ where $\sum_{i=1}^{m} a_{i} = 1976$

$\sqrt n < n!^\frac1n\ \forall \ n$

Prove that $\frac{\ 1}{a^2+b^2+ab}+\frac{\ 1}{b^2+c^2+bc}+\ \frac{\ 1}{c^2+a^2+ca}\ge\ \ \frac{\ 9}{\left(a+b+c\right)^2}$.

Chrystal's proof of the arithmetic-mean-geometric-mean inequality

Why AM-GM method can't be used to calculate the minimum value of $3\sin^2x+27\csc^2x$?

Find a good approximation of $r(x)$ for a proof

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