Question

A triangle has sides $a$, $b$, $c$ and medians $m_a$, $m_b$, $m_c$. Show $(ab+bc+ca)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq 2\sqrt{3}(m_a+m_b+m_c)$

score 200 · Answer 1 · 2026-03-25 07:45:43

200

Views

A triangle has sides $a$, $b$, $c$ and medians $m_a$, $m_b$, $m_c$. Show $(ab+bc+ca)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq 2\sqrt{3}(m_a+m_b+m_c)$

Published on 25 Mar 2026 - 7:45

score 160 · Answer 2 · 2026-04-12 17:34:15

160

Views

The $\ell_2$ norm of two stochastic vectors

Published on 12 Apr 2026 - 17:34

score 153 · Answer 3 · 2026-04-11 01:05:32

153

Views

Proof verification: For $a$, $b$, $c$ positive with $abc=1$, show $\sum_{\text{cyc}}\frac{1}{a^3(b+c)}\geq \frac32$

Published on 11 Apr 2026 - 1:05

score 91 · Answer 4 · 2026-04-13 15:26:03

91

Views

Show that $C=\{x \in \mathbb{R}^4 \mid x^TAx \geq 1\}$ is not empty?

Published on 13 Apr 2026 - 15:26

score 61 · Answer 5 · 2026-04-04 06:01:35

61

Views

For $(z_n)$ complex, $\limsup\limits_nn|z_n-1|$ finite iff $\limsup\limits_nn|\log(z_n)|$ finite

Published on 04 Apr 2026 - 6:01

score 119 · Answer 6 · 2018-12-17 07:36:35

119

Views

How to prove the Inequality $\sqrt[n]{b}-\sqrt[n]{a}<\sqrt[n]{b-a}$?

Published on 17 Dec 2018 - 7:36

score 906 · Answer 7 · 2026-04-13 01:20:58

906

Views

Is there an arithmetic proof to the AM GM Inequality for 3 variables?

Published on 13 Apr 2026 - 1:20

score 593 · Answer 8 · 2026-03-27 22:00:38

593

Views

Find an example of a random vector $X$ with its sub-gaussian norm much larger than any of its coordinates'.

Published on 27 Mar 2026 - 22:00

score 256 · Answer 9 · 2026-04-12 07:43:13

256

Views

Inequalities for standardized central moments of probability distributions

Published on 12 Apr 2026 - 7:43

score 1.7k · Answer 10 · 2026-04-12 05:11:53

1.7k

Views

How to prove upper bound for partial sum of binomial coefficients

Published on 12 Apr 2026 - 5:11

score 289 · Answer 11 · 2018-12-17 16:14:16

289

Views

Log-sum inequality

Published on 17 Dec 2018 - 16:14

score 179 · Answer 12 · 2026-04-09 07:34:12

179

Views

An inequality for positive definite matrix with trace 1

Published on 09 Apr 2026 - 7:34

score 110 · Answer 13 · 2026-04-04 06:03:18

110

Views

For every complex number $z$, $|z+1|\ge{1\over{\sqrt2}}$ or $|z^2+1|\ge1$: correct or incorrect?

Published on 04 Apr 2026 - 6:03

score 43 · Answer 14 · 2026-04-12 15:14:36

43

Views

finding the factors of a function and using calculus to find range where function's have 0's

Published on 12 Apr 2026 - 15:14

score 45 · Answer 15 · 2026-04-12 23:12:18

45

Views

derivative of function to see when it stops decreasing in order to check condition

Published on 12 Apr 2026 - 23:12

List Question

A triangle has sides $a$, $b$, $c$ and medians $m_a$, $m_b$, $m_c$. Show $(ab+bc+ca)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq 2\sqrt{3}(m_a+m_b+m_c)$

The $\ell_2$ norm of two stochastic vectors

Proof verification: For $a$, $b$, $c$ positive with $abc=1$, show $\sum_{\text{cyc}}\frac{1}{a^3(b+c)}\geq \frac32$

Show that $C=\{x \in \mathbb{R}^4 \mid x^TAx \geq 1\}$ is not empty?

For $(z_n)$ complex, $\limsup\limits_nn|z_n-1|$ finite iff $\limsup\limits_nn|\log(z_n)|$ finite

How to prove the Inequality $\sqrt[n]{b}-\sqrt[n]{a}<\sqrt[n]{b-a}$?

Is there an arithmetic proof to the AM GM Inequality for 3 variables?

Find an example of a random vector $X$ with its sub-gaussian norm much larger than any of its coordinates'.

Inequalities for standardized central moments of probability distributions

How to prove upper bound for partial sum of binomial coefficients

Log-sum inequality

An inequality for positive definite matrix with trace 1

For every complex number $z$, $|z+1|\ge{1\over{\sqrt2}}$ or $|z^2+1|\ge1$: correct or incorrect?

finding the factors of a function and using calculus to find range where function's have 0's

derivative of function to see when it stops decreasing in order to check condition

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