List questions from cauchy-schwarz-inequality

Published on 17 Apr 2026 - 8:23

68

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Prove the following inequality $a,b,c\in R_{+}^{*}$ and $2(a+b+c)=3$

Published on 16 Apr 2026 - 1:28

180

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Let $f (x$) = $\sqrt{−x^2 + 20x + 400} + \sqrt {x^2 − 20x}$. How many elements in the range of $f$ are integers?

Published on 17 Apr 2026 - 4:15

96

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Find all extrema of a complicated trigonometric function

Published on 14 Apr 2026 - 18:03

87

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Finding the operator norm of $\phi \in ((\ell^{2}, \|\cdot \|_{2}))^{*}$

Published on 14 Apr 2026 - 1:34

93

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Find the minimum value of $(\sin x+ \csc x)^2 + (\sec x + \cos x)^2$

Published on 15 Apr 2026 - 23:31

146

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Solve inequality

Published on 10 May 2026 - 16:07

94

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Given a, b, c are positive number, $abc=a+b+c$ prove $ab+4bc+9ac≥36$

Published on 12 Apr 2026 - 16:12

194

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How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?

Published on 10 May 2026 - 15:26

106

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shortest distance of $x^2 + y^2 = 4$ and $3x + 4y = 12$

Published on 13 May 2026 - 21:43

136

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Minimizing $9 \sec^2{x} + 16 \csc^2{x}$

Published on 15 Apr 2026 - 23:59

61

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an interesting inequality with Muirhead

Published on 10 May 2026 - 13:48

252

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Proving a reversed AM-HM inequality

Published on 10 May 2026 - 14:59

484

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Inequality on outer product

Published on 11 May 2026 - 6:12

226

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Does generalized Parseval identity series: $\langle g,h\rangle =\sum_{1}^{\infty}\langle g,e_i\rangle\langle e_i,h\rangle$ absolutely converge

Published on 09 Apr 2026 - 4:11

List Question

$\sum _{1}^{\infty}a_n^2/n$ converges then $(1/N)\sum_{1}^{N}a_n$ converges to zero.

Prove the following inequality $a,b,c\in R_{+}^{*}$ and $2(a+b+c)=3$

Let $f (x$) = $\sqrt{−x^2 + 20x + 400} + \sqrt {x^2 − 20x}$. How many elements in the range of $f$ are integers?

Find all extrema of a complicated trigonometric function

Finding the operator norm of $\phi \in ((\ell^{2}, \|\cdot \|_{2}))^{*}$

Find the minimum value of $(\sin x+ \csc x)^2 + (\sec x + \cos x)^2$

Solve inequality

Given a, b, c are positive number, $abc=a+b+c$ prove $ab+4bc+9ac≥36$

How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?

shortest distance of $x^2 + y^2 = 4$ and $3x + 4y = 12$

Minimizing $9 \sec^2{x} + 16 \csc^2{x}$

an interesting inequality with Muirhead

Proving a reversed AM-HM inequality

Inequality on outer product

Does generalized Parseval identity series: $\langle g,h\rangle =\sum_{1}^{\infty}\langle g,e_i\rangle\langle e_i,h\rangle$ absolutely converge

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