Question

Can I solve this blood question by re-arranging?

score 44 · Answer 1 · 2021-03-04 00:30:05

44

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Can I solve this blood question by re-arranging?

Published on 04 Mar 2021 - 0:30

score 146 · Answer 2 · 2021-03-26 00:21:22

146

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Rearrangement inequality with constraint

Published on 26 Mar 2021 - 0:21

score 116 · Answer 3 · 2021-06-16 16:31:13

116

Views

Prove that $a^3b^3 + b^3 + 1 \geq a^2b^2 + ab^3 + b$ (for real, positive $a$,$b$

Published on 16 Jun 2021 - 16:31

score 223 · Answer 4 · 2021-07-16 05:04:43

223

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Is there Inequality relating the arithmetic mean (AM) and the dot product

Published on 16 Jul 2021 - 5:04

score 252 · Answer 5 · 2026-03-25 15:45:27

252

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Using Rearrangement Inequality .

Published on 25 Mar 2026 - 15:45

score 242 · Answer 6 · 2021-08-03 16:10:46

242

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Show that $ \frac{x^2}{\sqrt{x^2+y^2}} + \frac{y^2}{\sqrt{y^2+z^2}} + \frac{z^2}{\sqrt{z^2+x^2}} \geq \frac{1}{\sqrt{2}}(x+y+z) $

Published on 03 Aug 2021 - 16:10

score 39 · Answer 7 · 2021-08-11 11:39:19

39

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Let $h_{1},h_{2},h_{3}$ be the altitudes and $m_{1},m_{2},m_{3}$ be the medians of the triangle ABC.

Published on 11 Aug 2021 - 11:39

score 223 · Answer 8 · 2021-09-13 16:37:38

223

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Let $x\geq y\geq z>0$. Prove that $ \frac {x^{2}y}{z} + \frac {y^{2}z}{x} + \frac {z^{2}x}{y}\geq x^{2} + y^{2} + z^{2}.$

Published on 13 Sep 2021 - 16:37

score 191 · Answer 9 · 2026-03-25 18:50:17

191

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Prove: $\left(\sqrt{a}+\sqrt{b}+\sqrt{c}\right)^2\ge\sqrt{3}\sum_{cyc}{\sqrt[4]{\frac{5ab}{c}+4a}}$

Published on 25 Mar 2026 - 18:50

score 197 · Answer 10 · 2021-10-22 13:48:23

197

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distance between sorted arrays

Published on 22 Oct 2021 - 13:48

score 129 · Answer 11 · 2021-11-29 08:15:25

129

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Inequality $a^4 + b^4 + c^4 + k(a^3b + b^3c + c^3a)$ $\ge (k + 1)(ab^3 + bc^3 + ca^3)$ where $k\in [0,1]$

Published on 29 Nov 2021 - 8:15

score 231 · Answer 12 · 2022-02-02 19:10:29

231

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Find a permutation $x_{\sigma(1)},\ldots,x_{\sigma(n)}$ of $x_1,\ldots,x_n$ that maximises $\sum_{k=1}^{n-1}\vert x_{\sigma(k)}-x_{\sigma(k+1)}\vert.$

Published on 02 Feb 2022 - 19:10

score 32 · Answer 13 · 2022-03-08 23:53:12

Permutation of $x_1,\ldots,x_n$ that gives least $y_1\sigma(x_1)+\ldots$ greater than $x_1y_1+\ldots:$ only two values $x_i,x_j$ must be swapped

score 193 · Answer 14 · 2022-03-13 13:07:32

193

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If for each $j\in\{1,\ldots,m\},\sum_{i=1}^m {x_i}^j = \sum_{i=1}^m {y_i}^j,$ then $(x_i)^{m}_{i=1}$ is a rearrangement of $(y_i)^{m}_{i=1}.$

Published on 13 Mar 2022 - 13:07

score 38 · Answer 15 · 2022-06-07 15:52:34

38

Views

Help with the inequality $a+{k}r\leq c+\sqrt{k}s$

Published on 07 Jun 2022 - 15:52

List Question

Can I solve this blood question by re-arranging?

Rearrangement inequality with constraint

Prove that $a^3b^3 + b^3 + 1 \geq a^2b^2 + ab^3 + b$ (for real, positive $a$,$b$

Is there Inequality relating the arithmetic mean (AM) and the dot product

Using Rearrangement Inequality .

Show that $ \frac{x^2}{\sqrt{x^2+y^2}} + \frac{y^2}{\sqrt{y^2+z^2}} + \frac{z^2}{\sqrt{z^2+x^2}} \geq \frac{1}{\sqrt{2}}(x+y+z) $

Let $h_{1},h_{2},h_{3}$ be the altitudes and $m_{1},m_{2},m_{3}$ be the medians of the triangle ABC.

Let $x\geq y\geq z>0$. Prove that $ \frac {x^{2}y}{z} + \frac {y^{2}z}{x} + \frac {z^{2}x}{y}\geq x^{2} + y^{2} + z^{2}.$

Prove: $\left(\sqrt{a}+\sqrt{b}+\sqrt{c}\right)^2\ge\sqrt{3}\sum_{cyc}{\sqrt[4]{\frac{5ab}{c}+4a}}$

distance between sorted arrays

Inequality $a^4 + b^4 + c^4 + k(a^3b + b^3c + c^3a)$ $\ge (k + 1)(ab^3 + bc^3 + ca^3)$ where $k\in [0,1]$

Find a permutation $x_{\sigma(1)},\ldots,x_{\sigma(n)}$ of $x_1,\ldots,x_n$ that maximises $\sum_{k=1}^{n-1}\vert x_{\sigma(k)}-x_{\sigma(k+1)}\vert.$

Permutation of $x_1,\ldots,x_n$ that gives least $y_1\sigma(x_1)+\ldots$ greater than $x_1y_1+\ldots:$ only two values $x_i,x_j$ must be swapped

If for each $j\in\{1,\ldots,m\},\sum_{i=1}^m {x_i}^j = \sum_{i=1}^m {y_i}^j,$ then $(x_i)^{m}_{i=1}$ is a rearrangement of $(y_i)^{m}_{i=1}.$

Help with the inequality $a+{k}r\leq c+\sqrt{k}s$

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