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

Published on 10 Jun 2020 - 14:11

198

Views

Power Mean Inequality based question

Published on 10 Jun 2020 - 20:04

92

Views

Cyclic Inequality $\frac{a^3}{(a+b)(a+c)}$

Published on 11 Jun 2020 - 10:19

102

Views

Help in proving this inequality

Published on 25 Mar 2026 - 19:10

321

Views

How to prove that $a + b + c + √3 \geq 8abc(\frac{1}{a^2 + 1} + \frac{1}{b^2+1} + \frac{1}{c^2 + 1})$ when $ab + bc + ca \geq 1$?

Published on 13 Jun 2020 - 2:57

141

Views

Prove that if $abc \geq 1$ and $a,b,c > 0$ then $\frac{1}{1 + a + b} + \frac{1}{1 + b + c} + \frac{1}{1 + c + a} \leq 1$

Published on 25 Mar 2026 - 9:43

28

Views

Let $a_1,\ldots,a_n \in [0,1)$ and $P:=(1-a_1)(1-a_2)\ldots(1-a_n)$. Find good lower-bound for $P$ in terms of $\|a\|_\infty$ and $\|a\|_2$

Published on 20 Jun 2020 - 7:42

229

Views

Find the minimum of $x^3+\frac{1}{x^2}$ for $x>0$

Published on 20 Jun 2020 - 12:28

100

Views

How to show $(a_1a_2\ldots a_n)^{\frac{1}{n}}\leq \frac{\sum_{i=1}^{n}a_i}{n}$

Published on 20 Jun 2020 - 17:17

147

Views

Prove: $\sqrt{\frac{bc}{a(3b+a)}} + \sqrt{\frac{ac}{b(3c+b)}} + \sqrt{\frac{ab}{c(3a+c)}} \ge \frac{3}{2}$.

Published on 25 Mar 2026 - 13:57

137

Views

Variation of Nesbitt Inequality with the geometric mean

Published on 22 Jun 2020 - 11:01

165

Views

Inequality of arithmetic mean of two sets

Published on 22 Jun 2020 - 12:07

133

Views

How AM-GM is applied here

Published on 22 Jun 2020 - 12:38

102

Views

Prove that $\frac{\sum_\text{cyc} x_1}{2020^2} \geq (n - 1)(\sum_\text{cyc} \frac{1}{x_1})$

Published on 22 Jun 2020 - 13:25

57

Views

$\left(\sum_i a_i\right)^2\ge (n-1)\sum_i a_i^2 + b\implies 2a_i a_j \ge b/(n-1) \quad (\forall i\ne j)$

Published on 24 Jun 2020 - 16:24

List Question

Problem manipulating AM-GM with 3 variables

Power Mean Inequality based question

Cyclic Inequality $\frac{a^3}{(a+b)(a+c)}$

Help in proving this inequality

How to prove that $a + b + c + √3 \geq 8abc(\frac{1}{a^2 + 1} + \frac{1}{b^2+1} + \frac{1}{c^2 + 1})$ when $ab + bc + ca \geq 1$?

Prove that if $abc \geq 1$ and $a,b,c > 0$ then $\frac{1}{1 + a + b} + \frac{1}{1 + b + c} + \frac{1}{1 + c + a} \leq 1$

Let $a_1,\ldots,a_n \in [0,1)$ and $P:=(1-a_1)(1-a_2)\ldots(1-a_n)$. Find good lower-bound for $P$ in terms of $\|a\|_\infty$ and $\|a\|_2$

Find the minimum of $x^3+\frac{1}{x^2}$ for $x>0$

How to show $(a_1a_2\ldots a_n)^{\frac{1}{n}}\leq \frac{\sum_{i=1}^{n}a_i}{n}$

Prove: $\sqrt{\frac{bc}{a(3b+a)}} + \sqrt{\frac{ac}{b(3c+b)}} + \sqrt{\frac{ab}{c(3a+c)}} \ge \frac{3}{2}$.

Variation of Nesbitt Inequality with the geometric mean

Inequality of arithmetic mean of two sets

How AM-GM is applied here

Prove that $\frac{\sum_\text{cyc} x_1}{2020^2} \geq (n - 1)(\sum_\text{cyc} \frac{1}{x_1})$

$\left(\sum_i a_i\right)^2\ge (n-1)\sum_i a_i^2 + b\implies 2a_i a_j \ge b/(n-1) \quad (\forall i\ne j)$

Trending Questions

Popular # Hahtags

Popular Questions