Question

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

score 92 · Answer 1 · 2026-03-25 03:02:35

92

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

Published on 25 Mar 2026 - 3:02

score 99 · Answer 2 · 2026-03-25 03:04:18

99

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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 25 Mar 2026 - 3:04

score 98 · Answer 3 · 2026-03-25 03:02:41

98

Views

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

Published on 25 Mar 2026 - 3:02

score 147 · Answer 4 · 2026-03-25 03:07:49

147

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

Published on 25 Mar 2026 - 3:07

score 97 · Answer 5 · 2026-03-25 03:07:30

97

Views

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

Published on 25 Mar 2026 - 3:07

score 193 · Answer 6 · 2026-03-25 04:43:27

193

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 Mar 2026 - 4:43

score 94 · Answer 7 · 2026-03-25 04:41:46

94

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

Published on 25 Mar 2026 - 4:41

score 101 · Answer 8 · 2026-03-25 04:42:31

101

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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 25 Mar 2026 - 4:42

score 112 · Answer 9 · 2026-03-25 03:04:33

112

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 25 Mar 2026 - 3:04

score 74 · Answer 10 · 2026-03-25 03:07:24

74

Views

Stuck on this cyclic 3-variables-inequality with constraint

Published on 25 Mar 2026 - 3:07

score 129 · Answer 11 · 2026-04-14 17:01:32

129

Views

Another Inequality

Published on 14 Apr 2026 - 17:01

score 335 · Answer 12 · 2026-04-08 21:06:49

335

Views

Proof of an inequality

Published on 08 Apr 2026 - 21:06

score 602 · Answer 13 · 2026-04-16 01:25:44

602

Views

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

Published on 16 Apr 2026 - 1:25

score 85 · Answer 14 · 2026-04-16 06:06:19

85

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

Published on 16 Apr 2026 - 6:06

score 122 · Answer 15 · 2026-05-07 06:57:12

122

Views

Chebyshev's sum inequality

Published on 07 May 2026 - 6:57

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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