List questions from uvw

Published on 16 Apr 2026 - 0:03

153

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What tools one should use for inequalities?

Published on 13 Apr 2026 - 12:26

262

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$ \frac {3 x y z}{(x+y) (y+z) (z+x)} + \sum\limits_{cycl}^{} \left(\frac {x+y}{x+y+ 2 z}\right)^2 \ge \frac {9}{8}.$

Published on 16 Apr 2026 - 14:45

208

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Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

Published on 17 Apr 2026 - 12:19

359

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Inequality with $abc=2$

Published on 11 Apr 2026 - 19:14

1.6k

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Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

Published on 15 Apr 2026 - 11:46

228

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

Published on 17 Apr 2026 - 2:20

792

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UVW method application of basic theorem

Published on 09 Apr 2026 - 0:35

95

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How to prove the given inequality using CS or AM GM HM inequality

Published on 15 Apr 2026 - 4:07

379

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Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

Published on 25 Mar 2026 - 3:21

328

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Prove $ \frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b} + \frac{36}{a + b + c} \geq 20 $

Published on 25 Mar 2026 - 4:42

144

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Prove $\Sigma_{cyc}(\frac{a}{b-c}-3)^4\ge193$

Published on 25 Mar 2026 - 16:02

363

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$\sqrt{24ab+25}+\sqrt{24bc+25}+\sqrt{24ca+25}\geq 21$ if $a+b+c=ab+bc+ca$?

Published on 25 Mar 2026 - 4:41

113

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Inequality with a+b+c=1 and $18(a^4+b^4+c^4)+6(a^2+b^2+c^2)+1\geq24(a^3+b^3+c^3)$

Published on 25 Mar 2026 - 4:42

136

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Inequalities, but working around an absolute value

Published on 25 Mar 2026 - 4:38

List Question

Double integral of $(y-2)^2$ over $\{(x,y)\in\mathbb{R}^2\colon x^2 +y^2 \le 6x\}$

What tools one should use for inequalities?

$ \frac {3 x y z}{(x+y) (y+z) (z+x)} + \sum\limits_{cycl}^{} \left(\frac {x+y}{x+y+ 2 z}\right)^2 \ge \frac {9}{8}.$

Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

Inequality with $abc=2$

Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

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

UVW method application of basic theorem

How to prove the given inequality using CS or AM GM HM inequality

Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

Prove $ \frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b} + \frac{36}{a + b + c} \geq 20 $

Prove $\Sigma_{cyc}(\frac{a}{b-c}-3)^4\ge193$

$\sqrt{24ab+25}+\sqrt{24bc+25}+\sqrt{24ca+25}\geq 21$ if $a+b+c=ab+bc+ca$?

Inequality with a+b+c=1 and $18(a^4+b^4+c^4)+6(a^2+b^2+c^2)+1\geq24(a^3+b^3+c^3)$

Inequalities, but working around an absolute value

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