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

Published on 20 Aug 2018 - 17:38

226

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If $x+y+z=3$ then $\sum x\sqrt{x^3+3y} \ge 6$

Published on 25 Mar 2026 - 6:06

131

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How to show that: $\left(\frac{mn+1}{m+1}\right)^{m+1} > n^m$

Published on 28 Aug 2018 - 16:57

118

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find the range $(x_{1}+x_{2}+\cdots+x_{2009})^2=4(x_{1}x_{2}+x_{2}x_{3}+\cdots+x_{2009}x_{1})^2$

Published on 30 Aug 2018 - 4:53

1.5k

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How to prove $(xyz)^{1/3} \le (x+y+z)/3$ using linear algebra

Published on 01 Sep 2018 - 12:47

85

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Prove this inequality for given conditions

Published on 02 Sep 2018 - 4:48

572

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Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$

Published on 25 Mar 2026 - 14:26

120

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Maximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)

Published on 02 Sep 2018 - 15:37

83

Views

How does the number $3$ help in this (probably Cauchy-based) inequality?

Published on 25 Mar 2026 - 4:54

118

Views

Show that for positive numbers a,b,c,d, $\sum_{cyc} ab \leq \frac{1}{4}\left(\sum_{cyc} a \right)^2$ and ...

Published on 25 Mar 2026 - 14:25

126

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How to prove this inequality using AM-GM?

Published on 25 Mar 2026 - 14:20

43

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How to prove the following inequality for a function?

Published on 25 Mar 2026 - 3:07

342

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P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

Published on 25 Mar 2026 - 1:40

206

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Inequality, how to know intuition behind it

Published on 14 Sep 2018 - 10:54

183

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Prove the inequality $\sqrt{\frac{a^2+1}{b+c}}+\sqrt{\frac{b^2+1}{a+c}}+\sqrt{\frac{c^2+1}{a+b}}\ge 3$

Published on 25 Mar 2026 - 1:40

List Question

$X>0$, $Y>0$ and $X^2+Y ^3\geq X^3+Y^4$. Prove that $X^3+Y ^3\leq 2$

If $x+y+z=3$ then $\sum x\sqrt{x^3+3y} \ge 6$

How to show that: $\left(\frac{mn+1}{m+1}\right)^{m+1} > n^m$

find the range $(x_{1}+x_{2}+\cdots+x_{2009})^2=4(x_{1}x_{2}+x_{2}x_{3}+\cdots+x_{2009}x_{1})^2$

How to prove $(xyz)^{1/3} \le (x+y+z)/3$ using linear algebra

Prove this inequality for given conditions

Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$

Maximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)

How does the number $3$ help in this (probably Cauchy-based) inequality?

Show that for positive numbers a,b,c,d, $\sum_{cyc} ab \leq \frac{1}{4}\left(\sum_{cyc} a \right)^2$ and ...

How to prove this inequality using AM-GM?

How to prove the following inequality for a function?

P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

Inequality, how to know intuition behind it

Prove the inequality $\sqrt{\frac{a^2+1}{b+c}}+\sqrt{\frac{b^2+1}{a+c}}+\sqrt{\frac{c^2+1}{a+b}}\ge 3$

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