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

Published on 25 Mar 2026 - 10:58

483

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Prove that for any real numbers $a, b, a^4+b^4+2 \geqslant 4ab$.

Published on 28 Jan 2018 - 22:01

208

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Inequality with $x^2+y^2+z^2=3$

Published on 17 Mar 2026 - 3:13

100

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Minimizing expression under constraint

Published on 24 Mar 2026 - 19:01

106

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Find the minimum value of an expression with three variables

Published on 25 Mar 2026 - 9:15

208

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AM/GM mean for $n=3$ using $n=4$

Published on 22 Mar 2026 - 8:42

129

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Find all the solutions $\in \Bbb R^+$ that satisfy $x(6-y)=9$, $y(6-z)=9$, $z(6-x)=9$

Published on 11 Feb 2018 - 19:48

353

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Prove that $(x-y)(y-z)(z-x) \leq \frac{1}{\sqrt{2}}$

Published on 23 Mar 2026 - 1:33

172

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Let $(x,y) \in \Bbb R^+$ Prove that $\Bigr(1+\frac{1}{x}\Bigl)\Bigr(1+\frac{1}{y}\Bigl)\ge \Bigr(1+\frac{2}{x+y}\Bigl)^2$

Published on 25 Mar 2026 - 4:43

78

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Proving inequality for all real $a$ and $b$.

Published on 23 Mar 2026 - 11:31

107

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maximum value of $a^2b$ condition is given

Published on 20 Mar 2026 - 5:03

172

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How do I prove this inequality: $a^2+b^2+c^2 \geq ab+bc+ac$?

Published on 23 Mar 2026 - 11:27

143

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Find the maximum value of given expression

Published on 24 Mar 2026 - 21:59

157

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Any ideas for this cyclic inequality?

Published on 24 Mar 2026 - 20:40

81

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how to solve the following inequality

Published on 22 Mar 2026 - 0:16

List Question

Proving an inequality with power

Prove that for any real numbers $a, b, a^4+b^4+2 \geqslant 4ab$.

Inequality with $x^2+y^2+z^2=3$

Minimizing expression under constraint

Find the minimum value of an expression with three variables

AM/GM mean for $n=3$ using $n=4$

Find all the solutions $\in \Bbb R^+$ that satisfy $x(6-y)=9$, $y(6-z)=9$, $z(6-x)=9$

Prove that $(x-y)(y-z)(z-x) \leq \frac{1}{\sqrt{2}}$

Let $(x,y) \in \Bbb R^+$ Prove that $\Bigr(1+\frac{1}{x}\Bigl)\Bigr(1+\frac{1}{y}\Bigl)\ge \Bigr(1+\frac{2}{x+y}\Bigl)^2$

Proving inequality for all real $a$ and $b$.

maximum value of $a^2b$ condition is given

How do I prove this inequality: $a^2+b^2+c^2 \geq ab+bc+ac$?

Find the maximum value of given expression

Any ideas for this cyclic inequality?

how to solve the following inequality

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