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

Published on 30 May 2020 - 1:31

39

Views

Find $W:= \frac{xy}{z}+\frac{yz}{x}+\frac{xz}{y} \rightarrow \inf$

Published on 30 May 2020 - 14:54

78

Views

Find $\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \to \min$

Published on 30 May 2020 - 20:44

72

Views

Question on Cauchy induction of AM GM Inequality

Published on 01 Jun 2020 - 13:30

103

Views

Inequality question.

Published on 26 Mar 2026 - 20:58

130

Views

Let $a,b,c>0$ with$ \frac{1}{a}+\frac{1}{b}+\frac{1}{c} = 1$. Prove that $(a + 1)(b + 1)(c + 1) \geq 64$

Published on 25 Mar 2026 - 9:43

88

Views

Inequality involving AM-GM but its wierd

Published on 25 Mar 2026 - 9:38

299

Views

Limitations of Arithmetic-Geometric Inequality?

Published on 04 Jun 2020 - 6:26

96

Views

Prove $(\frac{a}{b-c})^2+(\frac{b}{c-a})^2+(\frac{c}{a-b})^2 \geq 2$

Published on 28 Mar 2026 - 1:35

87

Views

Proof of inequality : $\frac{1}{a^3+b^3+abc}+\frac{1}{b^3+c^3+abc}+\frac{1}{c^3+a^3+abc}\le \frac{1}{abc}$

Published on 04 Jun 2020 - 11:45

82

Views

Proving the inequality that $\dfrac{x^2 + x^{-2}}{x-x^{-1}} \geq 2 \sqrt{2}$ for $x > 1$

Published on 04 Jun 2020 - 14:13

45

Views

Inequality question involving maximum value and three variables

Published on 07 Jun 2020 - 9:42

86

Views

Inequality involving difference of a power of 2 and 1

Published on 07 Jun 2020 - 10:44

240

Views

Let $a, b, c, d \in R^+$ such that $a + b + c + d = 1$. Prove that $\frac{a^3}{b+c}+\frac{b^3}{c+d}+\frac{c^3}{d+a}+\frac{d^3}{a+b} \geq \frac{1}{8}$

Published on 25 Mar 2026 - 17:41

180

Views

Weighted AM-GM inequality with reciprocal of natural numbers and exponents

Published on 08 Jun 2020 - 16:01

List Question

Olympiad Minimization Problem

Find $W:= \frac{xy}{z}+\frac{yz}{x}+\frac{xz}{y} \rightarrow \inf$

Find $\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \to \min$

Question on Cauchy induction of AM GM Inequality

Inequality question.

Let $a,b,c>0$ with$ \frac{1}{a}+\frac{1}{b}+\frac{1}{c} = 1$. Prove that $(a + 1)(b + 1)(c + 1) \geq 64$

Inequality involving AM-GM but its wierd

Limitations of Arithmetic-Geometric Inequality?

Prove $(\frac{a}{b-c})^2+(\frac{b}{c-a})^2+(\frac{c}{a-b})^2 \geq 2$

Proof of inequality : $\frac{1}{a^3+b^3+abc}+\frac{1}{b^3+c^3+abc}+\frac{1}{c^3+a^3+abc}\le \frac{1}{abc}$

Proving the inequality that $\dfrac{x^2 + x^{-2}}{x-x^{-1}} \geq 2 \sqrt{2}$ for $x > 1$

Inequality question involving maximum value and three variables

Inequality involving difference of a power of 2 and 1

Let $a, b, c, d \in R^+$ such that $a + b + c + d = 1$. Prove that $\frac{a^3}{b+c}+\frac{b^3}{c+d}+\frac{c^3}{d+a}+\frac{d^3}{a+b} \geq \frac{1}{8}$

Weighted AM-GM inequality with reciprocal of natural numbers and exponents

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