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

Published on 10 Jan 2017 - 14:55

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An Elementary Inequality Problem

Published on 18 Jan 2017 - 16:26

981

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How to Prove that $[(1+a)(1+b)(1+c)]^7$>$7^7a^4b^4c^4$

Published on 25 Mar 2026 - 19:06

83

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If $a,b,c$ are sides of a triangle then,

Published on 19 Jan 2017 - 15:18

1.6k

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Prove the inequality ${1 \over a^3 (b + c)} + {1 \over b^3 (a+c)} + {1 \over c^3 (a+b)} \ge \frac 32 $ given that $abc = 1$

Published on 25 Mar 2026 - 22:05

1.6k

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if : $abc=8 $ then : $(a+1)(b+1)(c+1)≥27$

Published on 25 Mar 2026 - 19:02

47

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prove that when : $(a+b)(c+d)(x+y)≥(\sqrt[3]{acx}+\sqrt[3]{bdy})^3$

Published on 25 Mar 2026 - 15:54

120

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Prove that $x+\frac{1}{x}\geq2$

Published on 26 Jan 2017 - 9:09

152

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Prove $(x+y+z)^8\ge 3^7(x^2+y^2+z^2)x^2y^2z^2$

Published on 25 Mar 2026 - 19:10

70

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minimum value of $ f(x) $ without the use of derivative

Published on 27 Jan 2017 - 14:38

152

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Inequalities with nice ideas

Published on 25 Mar 2026 - 23:35

190

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$a,b,c,d>0$ and $abcd=1$ prove $\sum \frac {1}{(1+a)(1+a^2)} \ge 1$

Published on 28 Jan 2017 - 18:46

154

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How to solve this problem using Jensen's inequality?

Published on 26 Mar 2026 - 1:00

119

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maximum value of expression $6bc+6abc+2ab+3ac$

Published on 02 Feb 2017 - 14:35

1.2k

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Let $a,b,c$ be positive real numbers such that $abc =1$

Published on 02 Feb 2017 - 16:14

List Question

Using AM-GM inequality

An Elementary Inequality Problem

How to Prove that $[(1+a)(1+b)(1+c)]^7$>$7^7a^4b^4c^4$

If $a,b,c$ are sides of a triangle then,

Prove the inequality ${1 \over a^3 (b + c)} + {1 \over b^3 (a+c)} + {1 \over c^3 (a+b)} \ge \frac 32 $ given that $abc = 1$

if : $abc=8 $ then : $(a+1)(b+1)(c+1)≥27$

prove that when : $(a+b)(c+d)(x+y)≥(\sqrt[3]{acx}+\sqrt[3]{bdy})^3$

Prove that $x+\frac{1}{x}\geq2$

Prove $(x+y+z)^8\ge 3^7(x^2+y^2+z^2)x^2y^2z^2$

minimum value of $ f(x) $ without the use of derivative

Inequalities with nice ideas

$a,b,c,d>0$ and $abcd=1$ prove $\sum \frac {1}{(1+a)(1+a^2)} \ge 1$

How to solve this problem using Jensen's inequality?

maximum value of expression $6bc+6abc+2ab+3ac$

Let $a,b,c$ be positive real numbers such that $abc =1$

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