Question

Proof of an inequality: is it correct?

score 67 · Answer 1 · 2026-03-25 01:16:49

67

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Proof of an inequality: is it correct?

Published on 25 Mar 2026 - 1:16

score 158 · Answer 2 · 2018-12-07 14:34:17

158

Views

Application of weighted AM-GM

Published on 07 Dec 2018 - 14:34

score 124 · Answer 3 · 2018-12-08 10:09:14

124

Views

Choosing suitable weights for AM-GM

Published on 08 Dec 2018 - 10:09

score 54 · Answer 4 · 2026-03-26 06:21:17

54

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Does $\alpha_j-(\Pi \alpha_i)^{1/d}=\beta_j-(\Pi \beta_i)^{1/d} $ force $\alpha_i=\beta_i$?

Published on 26 Mar 2026 - 6:21

score 94 · Answer 5 · 2026-03-25 03:21:27

94

Views

A simple proof for $\prod_{i=1}^d a_i+\prod_{i=1}^d b_i \le \prod_{i=1}^d (a_i^d+b_i^d)^{1/d}$?

Published on 25 Mar 2026 - 3:21

score 149 · Answer 6 · 2018-12-15 17:32:36

149

Views

Prove $x_1x_2…x_n \ge (n-1)^n$

Published on 15 Dec 2018 - 17:32

score 136 · Answer 7 · 2018-12-16 10:56:52

136

Views

Simple two variable am-gm inequality

Published on 16 Dec 2018 - 10:56

score 150 · Answer 8 · 2026-03-25 07:46:04

150

Views

If $ab+bc+ca=3$ for non-negative $a$, $b$, $c$, show that $\sum_{cyc}a^2b^2+\sum_{cyc}\frac{12a^2b^2c^2}{(a+b)^2}\ge 12abc$

Published on 25 Mar 2026 - 7:46

score 96 · Answer 9 · 2018-12-19 12:12:45

96

Views

How to show $7^{th}$ degree polynomial is non-positive in $[0,1]$

Published on 19 Dec 2018 - 12:12

score 99 · Answer 10 · 2018-12-19 14:56:29

99

Views

Find $a^3 + b^3 +c^3, $ given $a+b+c=12$ and $a^3 \cdot b^4 \cdot c^5 = 0.1 \cdot (600)^3$

Published on 19 Dec 2018 - 14:56

score 86 · Answer 11 · 2018-12-25 08:08:01

86

Views

Further terms of Taylor expansion for improved inequalities?

Published on 25 Dec 2018 - 8:08

score 168 · Answer 12 · 2026-03-25 05:03:03

168

Views

Inequality with $(x+y)(y+z)(z+w)(w+x)=1$

Published on 25 Mar 2026 - 5:03

score 193 · Answer 13 · 2018-12-30 22:44:41

193

Views

if $x-y =\sqrt{x}-\sqrt{y}$ with $x\neq y$ then $(1+\frac{1}{x})(1+\frac{1}{y})\geq 25$?

Published on 30 Dec 2018 - 22:44

score 118 · Answer 14 · 2018-12-31 10:46:39

118

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Prove $x_1^2 + x_2^3 + ... + x_{n - 1}^n + \frac{1}{x_1^2 x_2^3 ... x_{n - 1}^n} \geq n + (x_1 - 1)^2 + 2(x_2 - 1)^2 + ... + (n - 1)(x_{n - 1} - 1)^2$

Published on 31 Dec 2018 - 10:46

score 328 · Answer 15 · 2026-03-25 04:42:54

328

Views

Prove $ \frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b} + \frac{36}{a + b + c} \geq 20 $

Published on 25 Mar 2026 - 4:42

List Question

Proof of an inequality: is it correct?

Application of weighted AM-GM

Choosing suitable weights for AM-GM

Does $\alpha_j-(\Pi \alpha_i)^{1/d}=\beta_j-(\Pi \beta_i)^{1/d} $ force $\alpha_i=\beta_i$?

A simple proof for $\prod_{i=1}^d a_i+\prod_{i=1}^d b_i \le \prod_{i=1}^d (a_i^d+b_i^d)^{1/d}$?

Prove $x_1x_2…x_n \ge (n-1)^n$

Simple two variable am-gm inequality

If $ab+bc+ca=3$ for non-negative $a$, $b$, $c$, show that $\sum_{cyc}a^2b^2+\sum_{cyc}\frac{12a^2b^2c^2}{(a+b)^2}\ge 12abc$

How to show $7^{th}$ degree polynomial is non-positive in $[0,1]$

Find $a^3 + b^3 +c^3, $ given $a+b+c=12$ and $a^3 \cdot b^4 \cdot c^5 = 0.1 \cdot (600)^3$

Further terms of Taylor expansion for improved inequalities?

Inequality with $(x+y)(y+z)(z+w)(w+x)=1$

if $x-y =\sqrt{x}-\sqrt{y}$ with $x\neq y$ then $(1+\frac{1}{x})(1+\frac{1}{y})\geq 25$?

Prove $x_1^2 + x_2^3 + ... + x_{n - 1}^n + \frac{1}{x_1^2 x_2^3 ... x_{n - 1}^n} \geq n + (x_1 - 1)^2 + 2(x_2 - 1)^2 + ... + (n - 1)(x_{n - 1} - 1)^2$

Prove $ \frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b} + \frac{36}{a + b + c} \geq 20 $

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