Question

Extrema of a multivariable function with trigonometric functions.

score 288 · Answer 1 · 2026-02-23 09:27:55

288

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Extrema of a multivariable function with trigonometric functions.

Published on 23 Feb 2026 - 9:27

score 148 · Answer 2 · 2026-02-27 18:17:41

148

Views

Find the minimum value of $x$ s.t. $\sqrt{\left(\frac{x+y}{2}\right)^3}+\sqrt{\left(\frac{x-y}{2}\right)^3}=27$

Published on 27 Feb 2026 - 18:17

score 229 · Answer 3 · 2026-03-24 14:55:40

229

Views

A special case of Karamata's inequality to solve one or more Olympiad inequality?

Published on 24 Mar 2026 - 14:55

score 381 · Answer 4 · 2026-03-07 10:59:22

381

Views

Prove or Disprove this statement .

Published on 07 Mar 2026 - 10:59

score 84 · Answer 5 · 2026-03-24 15:04:03

84

Views

Proving an inequality involving real powers

Published on 24 Mar 2026 - 15:04

score 225 · Answer 6 · 2026-03-16 13:24:56

225

Views

Prove using Jensen's inequality that if $abcd=1$ then $\frac{1}{(1+a)^{2}}+\frac{1}{(1+b)^{2}}+\frac{1}{(1+c)^{2}}+\frac{1}{(1+d)^{2}} \geq 1$

Published on 16 Mar 2026 - 13:24

score 1.1k · Answer 7 · 2020-05-04 09:06:42

1.1k

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Why does this Olympiad inequality proving technique (Isolated Fudging) work?

Published on 04 May 2020 - 9:06

score 100 · Answer 8 · 2026-03-22 10:19:07

100

Views

If $0 < \alpha < \alpha + \delta < \beta < \frac\pi2$ then $\tan\alpha + \tan\beta > \tan(\alpha + \delta) + \tan(\beta - \delta).$

Published on 22 Mar 2026 - 10:19

score 436 · Answer 9 · 2016-10-30 00:48:54

436

Views

Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$

Published on 30 Oct 2016 - 0:48

score 91 · Answer 10 · 2017-02-07 07:06:52

91

Views

How do I prove this trigonometric inequality?

Published on 07 Feb 2017 - 7:06

score 337 · Answer 11 · 2017-02-08 11:33:24

337

Views

Given the positive real numbers $0\le a,b,c\le 2$ and $a+b+c=3$. Prove that $a^3+b^3+c^3\le 9$

Published on 08 Feb 2017 - 11:33

score 288 · Answer 12 · 2017-02-15 14:14:09

288

Views

Maximize $P=a^2+b^2+c^2+ab+ac+bc$

Published on 15 Feb 2017 - 14:14

score 704 · Answer 13 · 2017-02-18 18:13:56

704

Views

How to show $(a + b)^n \leq a^n + b^n$, where $a, b \geq 0$ and $n \in (0, 1]$?

Published on 18 Feb 2017 - 18:13

score 183 · Answer 14 · 2017-02-19 04:53:49

183

Views

If $a^2+b^2+c^2+d^2=4$ what is the range of $a^3+b^3+c^3+d^3$?

Published on 19 Feb 2017 - 4:53

score 140 · Answer 15 · 2026-03-14 12:54:11

140

Views

Prove or disprove the following generalization :$\sum_{i,j=1}^{n}f\left(a_{i}a_{j}\right)>n^{2}f\left(\sum_{i,j=1}^{n}\frac{a_{i}a_{j}}{n^{2}}\right)$

Published on 14 Mar 2026 - 12:54

List Question

Extrema of a multivariable function with trigonometric functions.

Find the minimum value of $x$ s.t. $\sqrt{\left(\frac{x+y}{2}\right)^3}+\sqrt{\left(\frac{x-y}{2}\right)^3}=27$

A special case of Karamata's inequality to solve one or more Olympiad inequality?

Prove or Disprove this statement .

Proving an inequality involving real powers

Prove using Jensen's inequality that if $abcd=1$ then $\frac{1}{(1+a)^{2}}+\frac{1}{(1+b)^{2}}+\frac{1}{(1+c)^{2}}+\frac{1}{(1+d)^{2}} \geq 1$

Why does this Olympiad inequality proving technique (Isolated Fudging) work?

If $0 < \alpha < \alpha + \delta < \beta < \frac\pi2$ then $\tan\alpha + \tan\beta > \tan(\alpha + \delta) + \tan(\beta - \delta).$

Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$

How do I prove this trigonometric inequality?

Given the positive real numbers $0\le a,b,c\le 2$ and $a+b+c=3$. Prove that $a^3+b^3+c^3\le 9$

Maximize $P=a^2+b^2+c^2+ab+ac+bc$

How to show $(a + b)^n \leq a^n + b^n$, where $a, b \geq 0$ and $n \in (0, 1]$?

If $a^2+b^2+c^2+d^2=4$ what is the range of $a^3+b^3+c^3+d^3$?

Prove or disprove the following generalization :$\sum_{i,j=1}^{n}f\left(a_{i}a_{j}\right)>n^{2}f\left(\sum_{i,j=1}^{n}\frac{a_{i}a_{j}}{n^{2}}\right)$

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