Question

Should I prove AGM inequality with 4 variables with Induction or Cauchy-Schwarz?

score 160 · Answer 1 · 2021-03-18 04:07:47

160

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Should I prove AGM inequality with 4 variables with Induction or Cauchy-Schwarz?

Published on 18 Mar 2021 - 4:07

score 602 · Answer 2 · 2026-03-26 19:20:03

602

Views

The inequality $\,2+\sqrt{\frac p2}\leq\sum\limits_\text{cyc}\sqrt{\frac{a^2+pbc}{b^2+c^2}}\,$ where $0\leq p\leq 2$ is: Probably true! Provably true?

Published on 26 Mar 2026 - 19:20

score 58 · Answer 3 · 2021-03-21 14:49:43

58

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Inequality with two variables and a conditional equation

Published on 21 Mar 2021 - 14:49

score 64 · Answer 4 · 2021-03-24 15:01:24

64

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$f\in C[a, b] $ Then show that $\frac{1}{M}\int_{a}^{b} f(x) \mathrm{dx} +m\int_{a}^{b} \frac1{f(x)} \mathrm{dx} \ge 2\sqrt{\frac mM} (b-a) $

Published on 24 Mar 2021 - 15:01

score 166 · Answer 5 · 2021-03-25 03:02:49

166

Views

Finding the maximum using inequalities

Published on 25 Mar 2021 - 3:02

score 141 · Answer 6 · 2021-03-25 08:15:04

141

Views

For positive integers $x$, $y$, and positive real $k$, if $\frac{x+1}{y+k}=\frac{y}{x}$, then $k\geq1$

Published on 25 Mar 2021 - 8:15

score 342 · Answer 7 · 2021-04-03 10:03:20

342

Views

Find the minimum value of $P=ab+bc+3ca+\dfrac{3}{a+b+c}$

Published on 03 Apr 2021 - 10:03

score 137 · Answer 8 · 2021-04-09 20:32:08

137

Views

Prove $x^{r}y^{1-r} ≤ rx + (1-r)y$ for $x,y > 0$ and $0<r≤1, r∈\mathbb{Q}$ using the AM-GM inequality

Published on 09 Apr 2021 - 20:32

score 57 · Answer 9 · 2026-03-31 22:47:52

57

Views

How to proceed further with the following inequality problem that can be used by the arithmetic and geometric inequality theorem

Published on 31 Mar 2026 - 22:47

score 49 · Answer 10 · 2021-04-19 15:59:18

49

Views

Find the least value of $\frac{1}{x}+\frac{3}{y}+\frac{5}{z}$

Published on 19 Apr 2021 - 15:59

score 2.9k · Answer 11 · 2021-04-21 10:03:32

2.9k

Views

$a^4+b^4+c^4+d^4=4abcd$ , prove that $a=b=c=d$.

Published on 21 Apr 2021 - 10:03

score 137 · Answer 12 · 2021-04-22 14:58:33

137

Views

strong inquality?

Published on 22 Apr 2021 - 14:58

score 142 · Answer 13 · 2021-05-01 08:10:30

142

Views

Revisit a familiar 3-variable inequality .

Published on 01 May 2021 - 8:10

score 75 · Answer 14 · 2021-05-01 10:23:20

75

Views

Let $0<a<b<1$ and $E=\log_{a}{\frac{2ab}{a+b}} + \log_{b}{\frac{2ab}{a+b}}$ Prove that $E>2$

Published on 01 May 2021 - 10:23

score 123 · Answer 15 · 2021-05-05 14:08:19

123

Views

$\sum_{i=1}^{n}{\frac{x_i}{\sqrt{1-x_i}}} \geq \sqrt{\frac{n}{n-1}}$ for $x_i \in \mathbb{R}_{++}$ such that $\sum_{i=1}^{n}{x_i}=1$

Published on 05 May 2021 - 14:08

List Question

Should I prove AGM inequality with 4 variables with Induction or Cauchy-Schwarz?

The inequality $\,2+\sqrt{\frac p2}\leq\sum\limits_\text{cyc}\sqrt{\frac{a^2+pbc}{b^2+c^2}}\,$ where $0\leq p\leq 2$ is: Probably true! Provably true?

Inequality with two variables and a conditional equation

$f\in C[a, b] $ Then show that $\frac{1}{M}\int_{a}^{b} f(x) \mathrm{dx} +m\int_{a}^{b} \frac1{f(x)} \mathrm{dx} \ge 2\sqrt{\frac mM} (b-a) $

Finding the maximum using inequalities

For positive integers $x$, $y$, and positive real $k$, if $\frac{x+1}{y+k}=\frac{y}{x}$, then $k\geq1$

Find the minimum value of $P=ab+bc+3ca+\dfrac{3}{a+b+c}$

Prove $x^{r}y^{1-r} ≤ rx + (1-r)y$ for $x,y > 0$ and $0<r≤1, r∈\mathbb{Q}$ using the AM-GM inequality

How to proceed further with the following inequality problem that can be used by the arithmetic and geometric inequality theorem

Find the least value of $\frac{1}{x}+\frac{3}{y}+\frac{5}{z}$

$a^4+b^4+c^4+d^4=4abcd$ , prove that $a=b=c=d$.

strong inquality?

Revisit a familiar 3-variable inequality .

Let $0<a<b<1$ and $E=\log_{a}{\frac{2ab}{a+b}} + \log_{b}{\frac{2ab}{a+b}}$ Prove that $E>2$

$\sum_{i=1}^{n}{\frac{x_i}{\sqrt{1-x_i}}} \geq \sqrt{\frac{n}{n-1}}$ for $x_i \in \mathbb{R}_{++}$ such that $\sum_{i=1}^{n}{x_i}=1$

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