List questions from cauchy-schwarz-inequality

Published on 27 Jul 2020 - 10:54

115

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Hint to an Inequality

Published on 28 Mar 2026 - 17:39

231

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Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

Published on 23 Feb 2026 - 4:42

81

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Finding a Mistake for a Particular Form of Inequality

Published on 28 Mar 2026 - 17:41

840

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If $a$, $b$, $c$, $d$ are positive reals so $(a+c)(b+d) = 1$, prove the following inequality would be greater than or equal to $\frac {1}{3}$.

Published on 25 Mar 2026 - 9:29

632

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Is the absolute value of a definite integral equal to the definite integral of the absolute value of the integrand?

Published on 30 Jul 2020 - 18:50

200

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Given that $x^2 + y^2 = 2x - 2y + 2$ , find the maximum value of $x^2 + y^2 + \sqrt{32}$ .

Published on 31 Jul 2020 - 5:13

66

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Find the $\sum\limits_{sym}ab$ maximum of the value

Published on 26 Mar 2026 - 1:28

227

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Inequality Challenge with $a+b+c=3$

Published on 25 Mar 2026 - 23:36

122

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How prove this inequality with $\sum\sqrt{a+b}\sum\frac{1}{\sqrt{2a+b+c}}\le\frac{9}{\sqrt{2}}$?

Published on 25 Mar 2026 - 19:10

285

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Prove this inequality $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$

Published on 25 Mar 2026 - 12:53

120

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$\sqrt{ab}$ + $\sqrt{bc}$ + $\sqrt{ac}$ $\leq$ $ \frac{3}{2}$

Published on 28 Mar 2026 - 20:58

307

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Inequality with $a+b+c=1$

Published on 25 Mar 2026 - 9:23

87

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Prove that $ a^{k} + b^{k} + c^{k} \ge a^{k-1}b + b^{k-1}c + c^{k-1}a$

Published on 25 Mar 2026 - 15:43

312

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What is the maximal value of $2 \sin x - 7 \cos x$?

Published on 07 Sep 2016 - 19:22

List Question

Finding the upper bound of a linear functional

Hint to an Inequality

Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

Finding a Mistake for a Particular Form of Inequality

If $a$, $b$, $c$, $d$ are positive reals so $(a+c)(b+d) = 1$, prove the following inequality would be greater than or equal to $\frac {1}{3}$.

Is the absolute value of a definite integral equal to the definite integral of the absolute value of the integrand?

Given that $x^2 + y^2 = 2x - 2y + 2$ , find the maximum value of $x^2 + y^2 + \sqrt{32}$ .

Find the $\sum\limits_{sym}ab$ maximum of the value

Inequality Challenge with $a+b+c=3$

How prove this inequality with $\sum\sqrt{a+b}\sum\frac{1}{\sqrt{2a+b+c}}\le\frac{9}{\sqrt{2}}$?

Prove this inequality $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$

$\sqrt{ab}$ + $\sqrt{bc}$ + $\sqrt{ac}$ $\leq$ $ \frac{3}{2}$

Inequality with $a+b+c=1$

Prove that $ a^{k} + b^{k} + c^{k} \ge a^{k-1}b + b^{k-1}c + c^{k-1}a$

What is the maximal value of $2 \sin x - 7 \cos x$?

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