List questions from uvw

Published on 18 Jul 2017 - 10:21

470

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Prove this trigonometric inequality about the angles of $\triangle ABC$

Published on 23 Jul 2017 - 4:24

88

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An algebraic inequality

Published on 23 Jul 2017 - 12:25

269

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show that $xyz(x-y)(x-z)(y-z)\le 27$

Published on 27 Jul 2017 - 3:19

153

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Inequality $ \sum_{cyc}\frac{b\sqrt{c}}{a(\sqrt{3c}+\sqrt{ab})}\geq \frac{3\sqrt{3}}{4} $

Published on 30 Jul 2017 - 7:45

930

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Maximum value of $a^3 + b^3 + c^3$

Published on 31 Jul 2017 - 9:01

145

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How prove this in equality with $abc=1$

Published on 26 Mar 2026 - 10:58

104

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Inequality - Maximize k such that

Published on 07 Aug 2017 - 6:29

107

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Inequality $(xy+z)^2+(yz+x)^2+(zx+y)^2\geq\sqrt{2}(x+y)(y+z)(z+x)$

Published on 08 Aug 2017 - 2:37

3.1k

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Inequality : $\sqrt[3]{\frac{x^3+y^3+z^3}{xyz}} + \sqrt{\frac{xy+yz+zx}{x^2+y^2+z^2}} \geq 1+\sqrt[3]{3}$

Published on 09 Aug 2017 - 3:01

358

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If $a+b+c=3$ show $a^2+b^2+c^2 \leq (27-15\sqrt{3})\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$

Published on 14 Aug 2017 - 22:39

525

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How to prove specific inequality, assuming $\prod\limits_{i=1}^{n}(a_{i}-1)=1$

Published on 25 Mar 2026 - 20:19

209

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Is it possible to prove that for $x,y,z \in \Bbb{R}$; if $x,y,z >0$ and $xyz=1$, then $(x+y+z)\ge 3$ without using the AM-GM inequality?

Published on 26 Mar 2026 - 9:50

178

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Prove this inequality $3(abc+4)\ge 5(ab+bc+ca)$

Published on 21 Sep 2017 - 16:55

85

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Find the minimum value of $ a/(1+b) + b/(1+a) + (1-a)(1-b)$

Published on 30 Sep 2017 - 11:33

List Question

Inequality $\sum_{cyc} \sqrt{\frac{a}{a+8}} \geq 1$

Prove this trigonometric inequality about the angles of $\triangle ABC$

An algebraic inequality

show that $xyz(x-y)(x-z)(y-z)\le 27$

Inequality $ \sum_{cyc}\frac{b\sqrt{c}}{a(\sqrt{3c}+\sqrt{ab})}\geq \frac{3\sqrt{3}}{4} $

Maximum value of $a^3 + b^3 + c^3$

How prove this in equality with $abc=1$

Inequality - Maximize k such that

Inequality $(xy+z)^2+(yz+x)^2+(zx+y)^2\geq\sqrt{2}(x+y)(y+z)(z+x)$

Inequality : $\sqrt[3]{\frac{x^3+y^3+z^3}{xyz}} + \sqrt{\frac{xy+yz+zx}{x^2+y^2+z^2}} \geq 1+\sqrt[3]{3}$

If $a+b+c=3$ show $a^2+b^2+c^2 \leq (27-15\sqrt{3})\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$

How to prove specific inequality, assuming $\prod\limits_{i=1}^{n}(a_{i}-1)=1$

Is it possible to prove that for $x,y,z \in \Bbb{R}$; if $x,y,z >0$ and $xyz=1$, then $(x+y+z)\ge 3$ without using the AM-GM inequality?

Prove this inequality $3(abc+4)\ge 5(ab+bc+ca)$

Find the minimum value of $ a/(1+b) + b/(1+a) + (1-a)(1-b)$

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