List questions from cauchy-schwarz-inequality

Published on 05 May 2019 - 11:51

312

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Inequality for $a,b,c>0$ $\sum_{cyc}\sqrt{\frac{a^3}{14a^2+4b^2}}\leq \sum_{cyc}\sqrt{\frac{a+b}{36}}$

Published on 25 Mar 2026 - 6:13

103

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show this $\sum_{cyc}\frac{x}{x^2-x+1}\le\frac{8}{3}$

Published on 25 Mar 2026 - 6:04

2.3k

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Solve $\sqrt{3}\sin(x)+\cos(x)-2=0$

Published on 10 May 2019 - 21:52

163

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Find $f(x)$ so that $\sum\limits_{cyc}a^{2}-f(x)\left(\prod_{sym}a-\prod_{sym}(1-a)\right)\geqq3(\frac{x}{2})^{2}$ .

Published on 25 Mar 2026 - 6:07

113

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Cyclic Olympiad Inequality

Published on 26 Mar 2026 - 23:57

159

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Let $f:[0,1]\to[1,3]$ be continuous. Prove $1 \leq \int_0^1 f(x)\,\mathrm dx \int_0^1 \frac{1}{f(x)}\, \mathrm dx\leq \frac{4}{3}$

Published on 25 Mar 2026 - 18:57

60

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Maximizing $f(x, y) = \sum_{k = 1}^{n} x_k y_k$ when $\sum_{k=1}^{n} x_k^2 = 1$ and $\sum_{k=1}^{n} y_k^2 = 4$

Published on 20 May 2019 - 19:00

79

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Proving an inequality given conditions.

Published on 27 Mar 2026 - 2:50

67

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Proving that $\int_0^1 \left(\frac{\partial T}{\partial z}(t,z)\right)^2\mathrm{d}z \geq 2 \int_0^1 T^2(t,z)\mathrm{d}z$

Published on 25 Mar 2026 - 18:59

54

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about Lagrange multipliers

Published on 26 Mar 2026 - 16:02

115

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Find minimum value of $P=17x^2+17y^2+16xy$

Published on 27 May 2019 - 10:14

144

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Minimizing a summation

Published on 28 May 2019 - 14:23

327

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Proof of Paley-Zygmund inequality

Published on 29 May 2019 - 4:13

153

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Holder unsuccessful here!

Published on 25 Mar 2026 - 8:05

List Question

Proof of Cauchy-Schwarz Inequality in probability form

Inequality for $a,b,c>0$ $\sum_{cyc}\sqrt{\frac{a^3}{14a^2+4b^2}}\leq \sum_{cyc}\sqrt{\frac{a+b}{36}}$

show this $\sum_{cyc}\frac{x}{x^2-x+1}\le\frac{8}{3}$

Solve $\sqrt{3}\sin(x)+\cos(x)-2=0$

Find $f(x)$ so that $\sum\limits_{cyc}a^{2}-f(x)\left(\prod_{sym}a-\prod_{sym}(1-a)\right)\geqq3(\frac{x}{2})^{2}$ .

Cyclic Olympiad Inequality

Let $f:[0,1]\to[1,3]$ be continuous. Prove $1 \leq \int_0^1 f(x)\,\mathrm dx \int_0^1 \frac{1}{f(x)}\, \mathrm dx\leq \frac{4}{3}$

Maximizing $f(x, y) = \sum_{k = 1}^{n} x_k y_k$ when $\sum_{k=1}^{n} x_k^2 = 1$ and $\sum_{k=1}^{n} y_k^2 = 4$

Proving an inequality given conditions.

Proving that $\int_0^1 \left(\frac{\partial T}{\partial z}(t,z)\right)^2\mathrm{d}z \geq 2 \int_0^1 T^2(t,z)\mathrm{d}z$

about Lagrange multipliers

Find minimum value of $P=17x^2+17y^2+16xy$

Minimizing a summation

Proof of Paley-Zygmund inequality

Holder unsuccessful here!

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