Question

$1/(51 +u^2) + 1/(51 +v^2) + 1/(51 +w^2)$ inequality

score 91 · Answer 1 · 2019-05-11 14:09:58

91

Views

$1/(51 +u^2) + 1/(51 +v^2) + 1/(51 +w^2)$ inequality

Published on 11 May 2019 - 14:09

score 98 · Answer 2 · 2019-06-03 11:39:35

98

Views

Find the minimum value of $\sum_{cyc}\frac{1}{\sqrt{a^2 - ab + 3b^2 + 1}}$ where $a, b, c > 0$ and $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \le 3$.

Published on 03 Jun 2019 - 11:39

score 97 · Answer 3 · 2019-06-27 07:12:50

97

Views

Equation for calculate right triangle's third point, Other 2 points and all three sides are known

Published on 27 Jun 2019 - 7:12

score 146 · Answer 4 · 2019-07-14 08:23:46

146

Views

find maximum and minimum of : $\tan (a)\tan (b)\tan (c)$

Published on 14 Jul 2019 - 8:23

score 96 · Answer 5 · 2019-07-17 08:59:16

96

Views

Given three positive numbers $a,b,c\in R_{+}^{*}$ prove the following inequality

Published on 17 Jul 2019 - 8:59

score 192 · Answer 6 · 2019-07-25 11:25:40

192

Views

How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?

Published on 25 Jul 2019 - 11:25

score 93 · Answer 7 · 2019-08-30 10:10:20

93

Views

Inequality $3\sin^{-1}\left(\frac{\pi^{1/3}}{2^{2/3}}\right)\leq a+b+c$ with some conditions

Published on 30 Aug 2019 - 10:10

score 100 · Answer 8 · 2019-09-14 13:42:30

100

Views

Calculate the maximum value of $\sum_{cyc}\frac{bc}{(b + c)^3(a^2 + 1)} $ where $a, b, c \in \mathbb R^+$ satisfying $abc = 1$.

Published on 14 Sep 2019 - 13:42

score 111 · Answer 9 · 2019-09-22 15:58:29

111

Views

Prove that $\frac{n}{3} \le \sum_{i = 1}^n\frac{(n - y)^2}{y^2(x_i^2 + x_i + 1) - 3ny(x_i + 1) + 3n^2} \le \sum_{i = 1}^n\frac{1}{x_i^2 + x_i + 1}$.

Published on 22 Sep 2019 - 15:58

score 73 · Answer 10 · 2019-09-29 15:39:29

73

Views

Stuck on this cyclic 3-variables-inequality with constraint

Published on 29 Sep 2019 - 15:39

score 124 · Answer 11 · 2014-05-14 13:06:21

124

Views

Another Inequality

Published on 14 May 2014 - 13:06

score 331 · Answer 12 · 2014-07-23 03:26:27

331

Views

Proof of an inequality

Published on 23 Jul 2014 - 3:26

score 599 · Answer 13 · 2014-07-30 05:39:27

599

Views

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

Published on 30 Jul 2014 - 5:39

score 82 · Answer 14 · 2014-11-16 07:33:00

82

Views

Find Min $P=\frac{a^4}{a+2b}+\frac{b^4}{b+2c}+\frac{c^4}{c+2a}$

Published on 16 Nov 2014 - 7:33

score 117 · Answer 15 · 2026-03-24 23:00:37

117

Views

Chebyshev's sum inequality

Published on 24 Mar 2026 - 23:00

List Question

$1/(51 +u^2) + 1/(51 +v^2) + 1/(51 +w^2)$ inequality

Find the minimum value of $\sum_{cyc}\frac{1}{\sqrt{a^2 - ab + 3b^2 + 1}}$ where $a, b, c > 0$ and $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \le 3$.

Equation for calculate right triangle's third point, Other 2 points and all three sides are known

find maximum and minimum of : $\tan (a)\tan (b)\tan (c)$

Given three positive numbers $a,b,c\in R_{+}^{*}$ prove the following inequality

How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?

Inequality $3\sin^{-1}\left(\frac{\pi^{1/3}}{2^{2/3}}\right)\leq a+b+c$ with some conditions

Calculate the maximum value of $\sum_{cyc}\frac{bc}{(b + c)^3(a^2 + 1)} $ where $a, b, c \in \mathbb R^+$ satisfying $abc = 1$.

Prove that $\frac{n}{3} \le \sum_{i = 1}^n\frac{(n - y)^2}{y^2(x_i^2 + x_i + 1) - 3ny(x_i + 1) + 3n^2} \le \sum_{i = 1}^n\frac{1}{x_i^2 + x_i + 1}$.

Stuck on this cyclic 3-variables-inequality with constraint

Another Inequality

Proof of an inequality

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

Find Min $P=\frac{a^4}{a+2b}+\frac{b^4}{b+2c}+\frac{c^4}{c+2a}$

Chebyshev's sum inequality

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