List questions from a-m-g-m-inequality

Published on 26 Mar 2020 - 19:20

50

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Does this "symmetric" inequality holds?

Published on 29 Mar 2020 - 16:44

67

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Proving $\sum_{i=1}^{n} \frac{a_{i}^2+a_{i+1}a_{i+2}}{a_{i}(a_{i+1}+a_{i+2})} \geq n.$

Published on 03 Apr 2020 - 9:11

138

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Prove $\frac{1+a^2}{1-a^2}+\frac{1+b^2}{1-b^2}+\frac{1+c^2}{1-c^2}\ge \frac{15}{4}$

Published on 25 Mar 2026 - 6:06

130

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Given $a, b, c>0$, prove $\frac{a^4}{a+b}+\frac{b^4}{b+c}+\frac{c^4}{c+a}\geq \frac{1}{2}(a^{2}c+b^{2}a+c^{2}b)$

Published on 25 Mar 2026 - 6:06

94

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Does $|f(\sqrt{xy})| \le |\frac{f(x)+f(y)}{2}|$ imply $f$ is a logarithm?

Published on 25 Mar 2026 - 17:26

707

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Number of ordered triplets (x,y,z) satisfying the given inequality

Published on 08 Apr 2020 - 10:05

687

Views

linear programming with logarithm

Published on 08 Apr 2020 - 21:24

622

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Minimize surface of cone with given volume without using derivatives

Published on 19 Apr 2020 - 15:41

170

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Doubt in solution of APMO 1998 Inequality problem

Published on 23 Apr 2020 - 16:17

114

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Inequality $a^ab^bc^c \geq (a+b-c)^a(b+c-a)^b(c+a-b)^c$

Published on 26 Mar 2026 - 11:17

31

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Proving $|\prod_{i=0}^n(x-x_i)|\leq\frac{n!}{4}(\frac{b-a}{n})^{n+1}$

Published on 23 Apr 2020 - 17:30

459

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Doubt in solution of problem in secrets in inequalities by pham kim hung

Published on 24 Apr 2020 - 2:56

69

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$\frac{a}{1+b^{2} c}+\frac{b}{1+c^{2} d}+\frac{c}{1+d^{2} a}+\frac{d}{1+a^{2} b} \geq 2 $

Published on 24 Apr 2020 - 12:31

70

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How to analyze the equation $(x-y)^2=2\big( (x+y)-2\sqrt{xy} \big)$?

Published on 26 Mar 2026 - 11:18

List Question

Find the maximum value of $x(9\sqrt{1+x^2}+13\sqrt{1-x^2})$

Does this "symmetric" inequality holds?

Proving $\sum_{i=1}^{n} \frac{a_{i}^2+a_{i+1}a_{i+2}}{a_{i}(a_{i+1}+a_{i+2})} \geq n.$

Prove $\frac{1+a^2}{1-a^2}+\frac{1+b^2}{1-b^2}+\frac{1+c^2}{1-c^2}\ge \frac{15}{4}$

Given $a, b, c>0$, prove $\frac{a^4}{a+b}+\frac{b^4}{b+c}+\frac{c^4}{c+a}\geq \frac{1}{2}(a^{2}c+b^{2}a+c^{2}b)$

Does $|f(\sqrt{xy})| \le |\frac{f(x)+f(y)}{2}|$ imply $f$ is a logarithm?

Number of ordered triplets (x,y,z) satisfying the given inequality

linear programming with logarithm

Minimize surface of cone with given volume without using derivatives

Doubt in solution of APMO 1998 Inequality problem

Inequality $a^ab^bc^c \geq (a+b-c)^a(b+c-a)^b(c+a-b)^c$

Proving $|\prod_{i=0}^n(x-x_i)|\leq\frac{n!}{4}(\frac{b-a}{n})^{n+1}$

Doubt in solution of problem in secrets in inequalities by pham kim hung

$\frac{a}{1+b^{2} c}+\frac{b}{1+c^{2} d}+\frac{c}{1+d^{2} a}+\frac{d}{1+a^{2} b} \geq 2 $

How to analyze the equation $(x-y)^2=2\big( (x+y)-2\sqrt{xy} \big)$?

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