List questions from rearrangement-inequality

Published on 25 Mar 2026 - 1:34

195

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$\frac {x_1^3}{y_1}+\frac {x_2^3}{y_3}+\ldots+\frac {x_n^3}{y_n}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x_1^2+x_2^2+\ldots+x_n^2) $

Published on 15 Sep 2018 - 19:13

83

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Prove $\sum \frac{a}{a+b^4+c^4} \le 1$

Published on 22 Mar 2026 - 16:01

71

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prove the statement

Published on 23 Mar 2026 - 21:42

124

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symmetrized rearrangement on sphere.

Published on 22 Mar 2026 - 4:54

141

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chebyshev's inequality - Question

Published on 22 Mar 2026 - 2:40

78

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Algebraic inequality for positive reals $a,b,c$

Published on 22 Mar 2026 - 18:52

221

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Prove that $\frac{a}{c\sqrt{a^2+1}}+\frac{b}{a\sqrt{b^2+1}}+\frac{c}{b\sqrt{c^2+1}}\ge \frac{3}{2}$

Published on 25 Mar 2026 - 4:59

580

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Chebyshev's Sum Inequality Proof

Published on 22 Mar 2026 - 11:54

77

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Inequality $\frac{a_1}{1^2}+\frac{a_2}{2^2}+...+\frac{a_n}{n^2}\ge\frac{1}{1}+\frac{1}{2}+...+\frac{1}{n}$

Published on 02 Feb 2019 - 8:53

786

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If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$

Published on 18 Feb 2019 - 17:15

167

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Find minimum of sum of product of sequences

Published on 22 Mar 2026 - 7:49

442

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Sum of cross terms vs sum of squares?

Published on 22 Mar 2026 - 8:54

67

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Prove, that for every real numbers $ x \ge y \ge z > 0 $, and $x+y+z=\frac{9}{2}, xyz=1$, the following inequality takes place

Published on 13 Mar 2019 - 11:31

217

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Prove $\sum \sqrt{\frac{a^2}{6a^2+5ab+b^2}}\le \frac{\sqrt{3}}{2}$

Published on 24 Mar 2026 - 23:46

List Question

Prove the inequality using Chebyshev's Inequality

$\frac {x_1^3}{y_1}+\frac {x_2^3}{y_3}+\ldots+\frac {x_n^3}{y_n}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x_1^2+x_2^2+\ldots+x_n^2) $

Prove $\sum \frac{a}{a+b^4+c^4} \le 1$

prove the statement

symmetrized rearrangement on sphere.

chebyshev's inequality - Question

Algebraic inequality for positive reals $a,b,c$

Prove that $\frac{a}{c\sqrt{a^2+1}}+\frac{b}{a\sqrt{b^2+1}}+\frac{c}{b\sqrt{c^2+1}}\ge \frac{3}{2}$

Chebyshev's Sum Inequality Proof

Inequality $\frac{a_1}{1^2}+\frac{a_2}{2^2}+...+\frac{a_n}{n^2}\ge\frac{1}{1}+\frac{1}{2}+...+\frac{1}{n}$

If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$

Find minimum of sum of product of sequences

Sum of cross terms vs sum of squares?

Prove, that for every real numbers $ x \ge y \ge z > 0 $, and $x+y+z=\frac{9}{2}, xyz=1$, the following inequality takes place

Prove $\sum \sqrt{\frac{a^2}{6a^2+5ab+b^2}}\le \frac{\sqrt{3}}{2}$

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