Question

Inequality. $\frac{a}{\sqrt{b}}+\frac{b}{\sqrt{c}}+\frac{c}{\sqrt{a}}\geq3$

score 474 · Answer 1 · 2013-10-24 07:43:00

474

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Inequality. $\frac{a}{\sqrt{b}}+\frac{b}{\sqrt{c}}+\frac{c}{\sqrt{a}}\geq3$

Published on 24 Oct 2013 - 7:43

score 2.1k · Answer 2 · 2026-03-25 17:44:42

2.1k

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How prove this inequality $\frac{x}{x+yz}+\frac{y}{y+zx}+\frac{z}{z+xy}\ge \frac{3}{2}$

Published on 25 Mar 2026 - 17:44

score 222 · Answer 3 · 2013-11-12 12:45:30

222

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How find this inequality minimum $\sum_{i=1}^{n}a^2_{i}-2\sum_{i=1}^{n-1}a_{i}a_{i+1}$

Published on 12 Nov 2013 - 12:45

score 108 · Answer 4 · 2017-04-14 13:45:38

108

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Find the minimum of the value $k$ such

Published on 14 Apr 2017 - 13:45

score 75 · Answer 5 · 2017-04-20 00:27:45

75

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Show $\sum_{\mbox{cyc}}\frac{3a^2+ac-c^2}{a^3+c^3}(a-c)^2 \geq \sum_{\mbox{cyc}}\frac{3a^2+ab-b^2}{a^3+b^3}(a-b)^2 \geq 0$

Published on 20 Apr 2017 - 0:27

score 777 · Answer 6 · 2017-04-21 05:34:21

777

Views

SOS: Proof of the AM-GM inequality

Published on 21 Apr 2017 - 5:34

score 135 · Answer 7 · 2017-05-07 19:54:31

135

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Prove that semi-perimeter $\geq a \cos A+b \cos B+c \cos C $

Published on 07 May 2017 - 19:54

score 175 · Answer 8 · 2017-05-08 22:54:24

175

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Minimum value of $\frac{x}{y^2}+\frac{y}{z^2}+\frac{z}{x^2}$

Published on 08 May 2017 - 22:54

score 99 · Answer 9 · 2026-03-25 16:20:34

99

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Given $a,b,c$. Prove inequality

Published on 25 Mar 2026 - 16:20

score 100 · Answer 10 · 2017-05-19 05:11:09

100

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Find the value of minimize $A=\sum_{cyc}\frac{x^4}{\left(x^2+y^2\right)\left(x+y\right)}$

Published on 19 May 2017 - 5:11

score 89 · Answer 11 · 2017-05-29 23:25:30

89

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Maximum of $xy(1-\frac{z^2}{(x+y)^2})+yz(1-\frac{x^2}{(y+z)^2})+zx(1-\frac{y^2}{(z+x)^2})$

Published on 29 May 2017 - 23:25

score 70 · Answer 12 · 2017-06-02 02:56:00

70

Views

Prove that inequality $6(\sum_{cyc}ab)+\sum_{cyc}a(b-c)^2$

Published on 02 Jun 2017 - 2:56

score 204 · Answer 13 · 2017-06-09 03:35:14

204

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Maximization of multivariable function $ M = \frac{a+1}{a^{2}+ 2a+2} + \frac{b+1}{b^{2}+ 2b+2} + \frac{c+1}{c^{2}+ 2c+2}$ subject to constraint

Published on 09 Jun 2017 - 3:35

score 439 · Answer 14 · 2017-06-11 10:02:13

439

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For $a,b,c>0$ . Prove $ (a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq 9+8\frac{(a-b)^{2}+(b-c)^{2}+(c-a)^{2}}{(a+b+c)^{2}}$

Published on 11 Jun 2017 - 10:02

score 706 · Answer 15 · 2017-06-12 09:34:51

706

Views

If $a^3+b^3+c^3=3$ so $2(a^2+b^2+c^2)-(ab+bc+ca) \geq 3$

Published on 12 Jun 2017 - 9:34

List Question

Inequality. $\frac{a}{\sqrt{b}}+\frac{b}{\sqrt{c}}+\frac{c}{\sqrt{a}}\geq3$

How prove this inequality $\frac{x}{x+yz}+\frac{y}{y+zx}+\frac{z}{z+xy}\ge \frac{3}{2}$

How find this inequality minimum $\sum_{i=1}^{n}a^2_{i}-2\sum_{i=1}^{n-1}a_{i}a_{i+1}$

Find the minimum of the value $k$ such

Show $\sum_{\mbox{cyc}}\frac{3a^2+ac-c^2}{a^3+c^3}(a-c)^2 \geq \sum_{\mbox{cyc}}\frac{3a^2+ab-b^2}{a^3+b^3}(a-b)^2 \geq 0$

SOS: Proof of the AM-GM inequality

Prove that semi-perimeter $\geq a \cos A+b \cos B+c \cos C $

Minimum value of $\frac{x}{y^2}+\frac{y}{z^2}+\frac{z}{x^2}$

Given $a,b,c$. Prove inequality

Find the value of minimize $A=\sum_{cyc}\frac{x^4}{\left(x^2+y^2\right)\left(x+y\right)}$

Maximum of $xy(1-\frac{z^2}{(x+y)^2})+yz(1-\frac{x^2}{(y+z)^2})+zx(1-\frac{y^2}{(z+x)^2})$

Prove that inequality $6(\sum_{cyc}ab)+\sum_{cyc}a(b-c)^2$

Maximization of multivariable function $ M = \frac{a+1}{a^{2}+ 2a+2} + \frac{b+1}{b^{2}+ 2b+2} + \frac{c+1}{c^{2}+ 2c+2}$ subject to constraint

For $a,b,c>0$ . Prove $ (a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq 9+8\frac{(a-b)^{2}+(b-c)^{2}+(c-a)^{2}}{(a+b+c)^{2}}$

If $a^3+b^3+c^3=3$ so $2(a^2+b^2+c^2)-(ab+bc+ca) \geq 3$

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