Question

Proving $\frac{1}{6}a+\frac{1}{3}b+\frac{1}{2}c \geq \frac{6abc}{3ab+bc+2ca}$ for positive $a$, $b$, $c$

score 125 · Answer 1 · 2026-04-15 20:31:14

125

Views

Proving $\frac{1}{6}a+\frac{1}{3}b+\frac{1}{2}c \geq \frac{6abc}{3ab+bc+2ca}$ for positive $a$, $b$, $c$

Published on 15 Apr 2026 - 20:31

score 345 · Answer 2 · 2026-05-10 15:56:22

345

Views

Bound $|x^TAy|$ in terms of $\|A\|$ and $|x^Ty|$

Published on 10 May 2026 - 15:56

score 193 · Answer 3 · 2026-04-17 08:07:46

193

Views

Prove the inequality $\frac{1}{1+x^2}+\frac{1}{1+y^2}+\frac{1}{1+xy} \geq \frac{3}{1+\frac{(x+y)^2}{4}}$ when $x^2+y^2=1$

Published on 17 Apr 2026 - 8:07

score 227 · Answer 4 · 2026-05-11 02:04:28

227

Views

Prove that $\int_0^1 (f'(x))^2dx \geq \frac{30}{31}$ when $f(f(x))=x^2$

Published on 11 May 2026 - 2:04

score 2k · Answer 5 · 2026-04-14 19:45:10

2k

Views

Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$

Published on 14 Apr 2026 - 19:45

score 181 · Answer 6 · 2026-05-10 17:50:09

181

Views

Let $n_1,\ldots,n_k$ be positive integers summing to $N$. What's an upper bound for $\sum_{i=1}^k1/\sqrt{n_i}$?

Published on 10 May 2026 - 17:50

score 74 · Answer 7 · 2026-04-11 21:50:23

74

Views

Cauchy-Schwarz Inequality question

Published on 11 Apr 2026 - 21:50

score 42 · Answer 8 · 2026-04-13 17:28:19

42

Views

Proving Cauchy-Schwartz inequality without the vanish assumption of inner products

Published on 13 Apr 2026 - 17:28

score 106 · Answer 9 · 2026-04-16 20:05:27

106

Views

Solve the equation $\frac{7x^2 - x + 4}{\sqrt{3x^2 - 1} + \sqrt{x^2 - x} - x\sqrt{x^2 + 1}} = 2\sqrt 2$.

Published on 16 Apr 2026 - 20:05

score 213 · Answer 10 · 2026-04-16 21:26:02

213

Views

Value of $\frac{1}{\sqrt{1+a^2}}+\frac{1}{\sqrt{1+b^2}}+\frac{1}{\sqrt{1+c^2}}+\frac{1}{\sqrt{1+d^2}}$

Published on 16 Apr 2026 - 21:26

score 334 · Answer 11 · 2026-04-13 21:29:12

334

Views

Tighter version of Cauchy-Schwarz?

Published on 13 Apr 2026 - 21:29

score 123 · Answer 12 · 2026-05-10 15:47:55

123

Views

Prove/disprove $\sum_{cyc}a\sqrt{\frac{(ca + 1)(ab + 1)}{bc + 1}} \ge 2$ where $a$, $b$, $c > 0$ and $a^2 + b^2 + c^2 = 1$

Published on 10 May 2026 - 15:47

score 26 · Answer 13 · 2026-04-15 22:42:00

26

Views

Check the Greatest and Smallest number

Published on 15 Apr 2026 - 22:42

score 297 · Answer 14 · 2026-04-11 20:20:12

297

Views

Proof for the bound of a complex exponential function

Published on 11 Apr 2026 - 20:20

score 71 · Answer 15 · 2026-05-10 13:49:02

71

Views

A three variable inequality doubt , can I consider the three variables into just one variable , and show the inequality.

Published on 10 May 2026 - 13:49

List Question

Proving $\frac{1}{6}a+\frac{1}{3}b+\frac{1}{2}c \geq \frac{6abc}{3ab+bc+2ca}$ for positive $a$, $b$, $c$

Bound $|x^TAy|$ in terms of $\|A\|$ and $|x^Ty|$

Prove the inequality $\frac{1}{1+x^2}+\frac{1}{1+y^2}+\frac{1}{1+xy} \geq \frac{3}{1+\frac{(x+y)^2}{4}}$ when $x^2+y^2=1$

Prove that $\int_0^1 (f'(x))^2dx \geq \frac{30}{31}$ when $f(f(x))=x^2$

Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$

Let $n_1,\ldots,n_k$ be positive integers summing to $N$. What's an upper bound for $\sum_{i=1}^k1/\sqrt{n_i}$?

Cauchy-Schwarz Inequality question

Proving Cauchy-Schwartz inequality without the vanish assumption of inner products

Solve the equation $\frac{7x^2 - x + 4}{\sqrt{3x^2 - 1} + \sqrt{x^2 - x} - x\sqrt{x^2 + 1}} = 2\sqrt 2$.

Value of $\frac{1}{\sqrt{1+a^2}}+\frac{1}{\sqrt{1+b^2}}+\frac{1}{\sqrt{1+c^2}}+\frac{1}{\sqrt{1+d^2}}$

Tighter version of Cauchy-Schwarz?

Prove/disprove $\sum_{cyc}a\sqrt{\frac{(ca + 1)(ab + 1)}{bc + 1}} \ge 2$ where $a$, $b$, $c > 0$ and $a^2 + b^2 + c^2 = 1$

Check the Greatest and Smallest number

Proof for the bound of a complex exponential function

A three variable inequality doubt , can I consider the three variables into just one variable , and show the inequality.

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