Question

Let $a,b,c$ be the sides of a triangle. The find maximum value $ \frac{A}{S^{2}}$

score 75 · Answer 1 · 2026-03-25 23:39:29

75

Views

Let $a,b,c$ be the sides of a triangle. The find maximum value $ \frac{A}{S^{2}}$

Published on 25 Mar 2026 - 23:39

score 126 · Answer 2 · 2026-03-26 22:55:20

126

Views

How to get the maximum of $f(x,y,z)=\frac{x+\sqrt{xy}+\sqrt[3]{xyz}}{x+y+z}, x,y,z\in\mathbb{R}_+$

Published on 26 Mar 2026 - 22:55

score 820 · Answer 3 · 2026-03-25 09:29:54

820

Views

Calculate the maximum value of $x^3y + y^3z + z^3x$ where $x + y + z = 4$ and $x, y, z \ge 0$.

Published on 25 Mar 2026 - 9:29

score 134 · Answer 4 · 2019-07-18 13:23:11

134

Views

Stronger than Am-Gm inequality

Published on 18 Jul 2019 - 13:23

score 39 · Answer 5 · 2019-07-19 07:09:17

39

Views

Prove that $2\sqrt{x+1} \ge 2\sqrt{x} + 1/\sqrt{x+1}$ for $x \ge 1$

Published on 19 Jul 2019 - 7:09

score 90 · Answer 6 · 2019-07-20 12:32:39

90

Views

Find the minimum value of $(\sin x+ \csc x)^2 + (\sec x + \cos x)^2$

Published on 20 Jul 2019 - 12:32

score 44 · Answer 7 · 2019-07-20 19:45:27

44

Views

For $a,b,t>0$, $0\leq\lambda\leq 1$, then $a^\lambda b^{1-\lambda}\leq\lambda t^{1/\lambda}a+(1-\lambda)t^{-1/(1-\lambda)}b$

Published on 20 Jul 2019 - 19:45

score 44 · Answer 8 · 2019-07-23 20:23:34

44

Views

AM GM inequality using a relation

Published on 23 Jul 2019 - 20:23

score 82 · Answer 9 · 2026-03-25 09:51:16

82

Views

Proving that $\frac{n_1a_1+\dots+n_ka_k}{n_1+\dots+n_k}\geq(a_1^{n_1}\dots a_k^{n_k})^{\frac{1}{n_1+\dots+n_k}}$

Published on 25 Mar 2026 - 9:51

score 90 · Answer 10 · 2019-07-25 15:57:06

90

Views

Showing $\left(\frac{\sum a_{i}+1}{2}\right)^{2}\geq \sum a_{i}^{2}.$

Published on 25 Jul 2019 - 15:57

score 990 · Answer 11 · 2019-07-26 01:36:45

990

Views

Trying to grasp the concept of homogeneous inequalities

Published on 26 Jul 2019 - 1:36

score 156 · Answer 12 · 2019-07-26 16:14:05

156

Views

Find the Range of $y=\frac{x+a}{x^2+bx+c^2}$

Published on 26 Jul 2019 - 16:14

score 52 · Answer 13 · 2026-03-25 09:50:17

52

Views

Maximum value of $\prod_{r=1}^n\cos a_r$ if $0\le a_1,\ldots,a_n\le\frac{\pi}{2}$ and $\prod_{r=1}^n\cot a_r = 1$

Published on 25 Mar 2026 - 9:50

score 323 · Answer 14 · 2019-08-06 04:41:49

323

Views

Prove the following inequality for any positive real number $x,y$

Published on 06 Aug 2019 - 4:41

score 165 · Answer 15 · 2026-03-25 09:23:54

165

Views

Inequalities: BMO 2009/10 Round 2

Published on 25 Mar 2026 - 9:23

List Question

Let $a,b,c$ be the sides of a triangle. The find maximum value $ \frac{A}{S^{2}}$

How to get the maximum of $f(x,y,z)=\frac{x+\sqrt{xy}+\sqrt[3]{xyz}}{x+y+z}, x,y,z\in\mathbb{R}_+$

Calculate the maximum value of $x^3y + y^3z + z^3x$ where $x + y + z = 4$ and $x, y, z \ge 0$.

Stronger than Am-Gm inequality

Prove that $2\sqrt{x+1} \ge 2\sqrt{x} + 1/\sqrt{x+1}$ for $x \ge 1$

Find the minimum value of $(\sin x+ \csc x)^2 + (\sec x + \cos x)^2$

For $a,b,t>0$, $0\leq\lambda\leq 1$, then $a^\lambda b^{1-\lambda}\leq\lambda t^{1/\lambda}a+(1-\lambda)t^{-1/(1-\lambda)}b$

AM GM inequality using a relation

Proving that $\frac{n_1a_1+\dots+n_ka_k}{n_1+\dots+n_k}\geq(a_1^{n_1}\dots a_k^{n_k})^{\frac{1}{n_1+\dots+n_k}}$

Showing $\left(\frac{\sum a_{i}+1}{2}\right)^{2}\geq \sum a_{i}^{2}.$

Trying to grasp the concept of homogeneous inequalities

Find the Range of $y=\frac{x+a}{x^2+bx+c^2}$

Maximum value of $\prod_{r=1}^n\cos a_r$ if $0\le a_1,\ldots,a_n\le\frac{\pi}{2}$ and $\prod_{r=1}^n\cot a_r = 1$

Prove the following inequality for any positive real number $x,y$

Inequalities: BMO 2009/10 Round 2

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