List questions from cauchy-schwarz-inequality

Published on 28 Mar 2026 - 19:39

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Prove the inequality $\sqrt{a^2+b^2}+\sqrt{c^2+b^2}+\sqrt{a^2+c^2}<1+\frac{\sqrt2}{2}$

Published on 26 Mar 2026 - 17:54

156

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Prove the inequality $\frac a{a+b^2}+\frac b{b+c^2}+\frac c{c+a^2}\le\frac14\left(\frac1a+\frac1b+\frac1c\right)$

Published on 25 Mar 2026 - 23:42

151

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Schwarz's Inequality

Published on 22 Sep 2016 - 8:22

887

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$ab(a+b) + bc(b+c) + ac(a+c) \geq \frac{2}{3}(a^{2}+b^{2}+c^{2})+ 4abc$ for $\frac1a+\frac1b+\frac1c=3$ and $a,b,c>0$

Published on 26 Mar 2026 - 1:23

297

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If $a$, $b$ and $c$ are three positive real numbers, prove that $\frac{a^2+1}{b+c}+\frac{b^2+1}{c+a}+\frac{c^2+1}{a+b} ≥ 3$

Published on 28 Mar 2026 - 19:39

94

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A problem on inequality and number theory

Published on 08 Oct 2016 - 7:39

374

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If $abc=1$ so $\sum\limits_{cyc}\frac{a}{\sqrt{a+b^2}}\geq\frac{3}{\sqrt2}$

Published on 25 Mar 2026 - 11:14

76

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Inequality with the constraint $xy=x+y$

Published on 12 Oct 2016 - 15:09

83

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Solving Inequalities similar to Nesbitt's

Published on 18 Oct 2016 - 17:35

88

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Non - symetric inequality in 3 variables

Published on 25 Mar 2026 - 11:11

135

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Show $\frac1{a^2+a+1}+\frac1{b^2+b+1}+\frac1{c^2+c+1}\ge1$

Published on 25 Oct 2016 - 1:22

1.1k

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Prove inequality $ \frac{(x+y-1)^2}{z}+\frac{(x+z-1)^2}{y}+\frac{(y+z-1)^2}{x} \geq 12 $

Published on 25 Mar 2026 - 19:07

5.5k

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Cauchy-Schwarz Inequality and series proof

Published on 28 Oct 2016 - 17:13

126

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The least positive real number $k$ for which $k\left(\sqrt{(x+y)(y+z)(z+x)}\right)\geq x\sqrt{y}+y\sqrt{z}+z\sqrt{x}$

Published on 26 Mar 2026 - 1:23

List Question

inequality for positive number $a+b+c=3$

Prove the inequality $\sqrt{a^2+b^2}+\sqrt{c^2+b^2}+\sqrt{a^2+c^2}<1+\frac{\sqrt2}{2}$

Prove the inequality $\frac a{a+b^2}+\frac b{b+c^2}+\frac c{c+a^2}\le\frac14\left(\frac1a+\frac1b+\frac1c\right)$

Schwarz's Inequality

$ab(a+b) + bc(b+c) + ac(a+c) \geq \frac{2}{3}(a^{2}+b^{2}+c^{2})+ 4abc$ for $\frac1a+\frac1b+\frac1c=3$ and $a,b,c>0$

If $a$, $b$ and $c$ are three positive real numbers, prove that $\frac{a^2+1}{b+c}+\frac{b^2+1}{c+a}+\frac{c^2+1}{a+b} ≥ 3$

A problem on inequality and number theory

If $abc=1$ so $\sum\limits_{cyc}\frac{a}{\sqrt{a+b^2}}\geq\frac{3}{\sqrt2}$

Inequality with the constraint $xy=x+y$

Solving Inequalities similar to Nesbitt's

Non - symetric inequality in 3 variables

Show $\frac1{a^2+a+1}+\frac1{b^2+b+1}+\frac1{c^2+c+1}\ge1$

Prove inequality $ \frac{(x+y-1)^2}{z}+\frac{(x+z-1)^2}{y}+\frac{(y+z-1)^2}{x} \geq 12 $

Cauchy-Schwarz Inequality and series proof

The least positive real number $k$ for which $k\left(\sqrt{(x+y)(y+z)(z+x)}\right)\geq x\sqrt{y}+y\sqrt{z}+z\sqrt{x}$

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