Question

How does the number $3$ help in this (probably Cauchy-based) inequality?

score 83 · Answer 1 · 2026-03-25 04:54:36

83

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How does the number $3$ help in this (probably Cauchy-based) inequality?

Published on 25 Mar 2026 - 4:54

score 92 · Answer 2 · 2026-03-25 07:43:05

92

Views

Prove the identity in inner product space

Published on 25 Mar 2026 - 7:43

score 166 · Answer 3 · 2018-09-11 11:20:38

166

Views

Inequality with $\frac{x^2+y^2+z^2+w}{(x+y+z)^3}$

Published on 11 Sep 2018 - 11:20

score 60 · Answer 4 · 2018-09-11 22:07:45

60

Views

For $1 \leq k\leq n$ if $x_k$ is a non-zero real number and $x_1^2+\ldots +x_n^2=X.$ Is it true $x_1+\ldots +x_n \leq X^{\frac{1}{2}} ?$

Published on 11 Sep 2018 - 22:07

score 342 · Answer 5 · 2026-03-25 01:40:06

342

Views

P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

Published on 25 Mar 2026 - 1:40

score 1.4k · Answer 6 · 2018-09-12 16:59:02

1.4k

Views

Show Cauchy-Schwarz inequality from triangle inequality for $\mathbb{C}$-vector space

Published on 12 Sep 2018 - 16:59

score 68 · Answer 7 · 2018-09-13 06:25:30

68

Views

What is the minimum value of $\sum_{n=1}^{\infty}a_n^2$ $\forall a_n >0$ such that $\sum_{n=1}^{\infty}a_n=A$?

Published on 13 Sep 2018 - 6:25

score 179 · Answer 8 · 2026-03-25 06:51:39

179

Views

Lagrange multiplier method on Banach spaces (in Dirac notation)

Published on 25 Mar 2026 - 6:51

score 196 · Answer 9 · 2026-03-25 07:46:29

196

Views

$\frac {x_1^3}{y_1}+\frac {x_2^3}{y_3}+\ldots+\frac {x_n^3}{y_n}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x_1^2+x_2^2+\ldots+x_n^2) $

Published on 25 Mar 2026 - 7:46

score 183 · Answer 10 · 2026-03-25 01:40:04

183

Views

Prove the inequality $\sqrt{\frac{a^2+1}{b+c}}+\sqrt{\frac{b^2+1}{a+c}}+\sqrt{\frac{c^2+1}{a+b}}\ge 3$

Published on 25 Mar 2026 - 1:40

score 2.1k · Answer 11 · 2018-09-21 22:17:39

2.1k

Views

Prove Cauchy-Schwarz with AM-GM for three variables

Published on 21 Sep 2018 - 22:17

score 1.8k · Answer 12 · 2018-09-24 18:05:18

1.8k

Views

Metric on Cartesian Product

Published on 24 Sep 2018 - 18:05

score 134 · Answer 13 · 2026-03-25 22:05:09

134

Views

If $\sum\limits_{\text{cyc}}x=\frac\pi2$, then $2\sqrt{\sum\limits_{\text{cyc}}\tan x}\le\sum\limits_{\text{cyc}}\frac{\sqrt{\tan x}}{\cos x}$

Published on 25 Mar 2026 - 22:05

score 160 · Answer 14 · 2026-03-26 04:52:22

160

Views

A very strange algebra problem with four numbers with an average 1.

Published on 26 Mar 2026 - 4:52

score 1.3k · Answer 15 · 2018-09-26 13:46:21

1.3k

Views

Understanding the proof of Cauchy-Schwartz inequality

Published on 26 Sep 2018 - 13:46

List Question

How does the number $3$ help in this (probably Cauchy-based) inequality?

Prove the identity in inner product space

Inequality with $\frac{x^2+y^2+z^2+w}{(x+y+z)^3}$

For $1 \leq k\leq n$ if $x_k$ is a non-zero real number and $x_1^2+\ldots +x_n^2=X.$ Is it true $x_1+\ldots +x_n \leq X^{\frac{1}{2}} ?$

P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

Show Cauchy-Schwarz inequality from triangle inequality for $\mathbb{C}$-vector space

What is the minimum value of $\sum_{n=1}^{\infty}a_n^2$ $\forall a_n >0$ such that $\sum_{n=1}^{\infty}a_n=A$?

Lagrange multiplier method on Banach spaces (in Dirac notation)

$\frac {x_1^3}{y_1}+\frac {x_2^3}{y_3}+\ldots+\frac {x_n^3}{y_n}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x_1^2+x_2^2+\ldots+x_n^2) $

Prove the inequality $\sqrt{\frac{a^2+1}{b+c}}+\sqrt{\frac{b^2+1}{a+c}}+\sqrt{\frac{c^2+1}{a+b}}\ge 3$

Prove Cauchy-Schwarz with AM-GM for three variables

Metric on Cartesian Product

If $\sum\limits_{\text{cyc}}x=\frac\pi2$, then $2\sqrt{\sum\limits_{\text{cyc}}\tan x}\le\sum\limits_{\text{cyc}}\frac{\sqrt{\tan x}}{\cos x}$

A very strange algebra problem with four numbers with an average 1.

Understanding the proof of Cauchy-Schwartz inequality

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