List questions from cauchy-schwarz-inequality

Published on 25 Mar 2026 - 11:53

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Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.

Published on 22 Mar 2026 - 10:14

185

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Prove that if $a$ and $b$ satisfy $2a+4b=1$, then $a^2+b^2\ge \frac {1}{20}$

Published on 25 Mar 2026 - 21:49

61

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Solving without squaring

Published on 24 Mar 2026 - 20:30

141

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Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$

Published on 25 Mar 2026 - 6:22

78

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Why the following equality is true?

Published on 25 Mar 2026 - 6:08

82

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Finding a scalar product on $C([-1,1], \mathbb{R})$ given an example of Cauchy-Shwarz applied to it

Published on 25 Mar 2026 - 21:31

193

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Prove that $\sqrt{x^2+yz}+\sqrt{y^2+xz}+\sqrt{z^2+xy} \le 3$

Published on 24 Mar 2026 - 23:48

84

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Proving $ \frac {(a+b)^2 }{\sqrt{(a+b)^2 +1}} < 2 \left( \frac {a^2 }{\sqrt{ a^2 +1}} + \frac{b^2 } {\sqrt{ b^2 +1 }} \right) $

Published on 25 Mar 2026 - 6:07

150

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Quadratic Equations(determine the nature of roots)

Published on 22 Mar 2026 - 14:12

2.5k

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Why is the Cauchy Schwarz inequality a special case of Holder's inequality?

Published on 22 Mar 2026 - 9:56

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

70

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Matrix Norm Inequalities

Published on 16 Mar 2026 - 20:34

251

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Interesting inequalities that can be derived from Cauchy-Schwarz

Published on 17 Mar 2026 - 18:26

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

List Question

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

Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.

Prove that if $a$ and $b$ satisfy $2a+4b=1$, then $a^2+b^2\ge \frac {1}{20}$

Solving without squaring

Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$

Why the following equality is true?

Finding a scalar product on $C([-1,1], \mathbb{R})$ given an example of Cauchy-Shwarz applied to it

Prove that $\sqrt{x^2+yz}+\sqrt{y^2+xz}+\sqrt{z^2+xy} \le 3$

Proving $ \frac {(a+b)^2 }{\sqrt{(a+b)^2 +1}} < 2 \left( \frac {a^2 }{\sqrt{ a^2 +1}} + \frac{b^2 } {\sqrt{ b^2 +1 }} \right) $

Quadratic Equations(determine the nature of roots)

Why is the Cauchy Schwarz inequality a special case of Holder's inequality?

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

Matrix Norm Inequalities

Interesting inequalities that can be derived from Cauchy-Schwarz

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

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