List questions from tangent-line-method

Published on 20 Mar 2013 - 23:09

193

Views

A more elementary proof that if $x_i>0$ for $1\leq i\leq n$, and $\sum x_i=1$, then $(x_1+\frac{1}{x_1})\cdots(x_n+\frac{1}{x_n})\geq(n+\frac1n)^n$

Published on 31 Jul 2020 - 18:12

286

Views

Inequality with a High Degree Constraint

Published on 01 Aug 2020 - 6:00

81

Views

Dubious proof of an Inequality

Published on 03 Aug 2020 - 13:02

256

Views

Proving $(1+a^2)(1+b^2)(1+c^2)\geq8 $

Published on 04 Aug 2020 - 10:45

70

Views

Is this Factorization?

Published on 06 Aug 2020 - 11:10

156

Views

cyclic rational inequalities $\frac{1}{a^2+3}+\frac{1}{b^2+3}+\frac{1}{c^2+3}\leq\frac{27}{28}$ when $a+b+c=1$

Published on 23 Oct 2020 - 15:38

161

Views

Inequality with $\sum a^5+8\sum ab$

Published on 13 Apr 2021 - 14:04

120

Views

Prove that: $(a^5-2a+4)(b^5-2b+4)(c^5-2c+4)\ge9(ab+bc+ca)$

Published on 01 Jul 2021 - 4:29

251

Views

Using Rearrangement Inequality .

Published on 22 Jul 2021 - 8:58

280

Views

Prove or disprove $\sum\limits_{1\le i < j \le n} \frac{x_ix_j}{1-x_i-x_j} \le \frac18$ for $\sum\limits_{i=1}^n x_i = \frac12$($x_i\ge 0, \forall i$)

Published on 02 Jun 2022 - 14:09

List Question

Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$

A more elementary proof that if $x_i>0$ for $1\leq i\leq n$, and $\sum x_i=1$, then $(x_1+\frac{1}{x_1})\cdots(x_n+\frac{1}{x_n})\geq(n+\frac1n)^n$

Inequality with a High Degree Constraint

Dubious proof of an Inequality

Proving $(1+a^2)(1+b^2)(1+c^2)\geq8 $

Is this Factorization?

cyclic rational inequalities $\frac{1}{a^2+3}+\frac{1}{b^2+3}+\frac{1}{c^2+3}\leq\frac{27}{28}$ when $a+b+c=1$

Inequality with $\sum a^5+8\sum ab$

Prove that: $(a^5-2a+4)(b^5-2b+4)(c^5-2c+4)\ge9(ab+bc+ca)$

Using Rearrangement Inequality .

Prove or disprove $\sum\limits_{1\le i < j \le n} \frac{x_ix_j}{1-x_i-x_j} \le \frac18$ for $\sum\limits_{i=1}^n x_i = \frac12$($x_i\ge 0, \forall i$)

Trending Questions

Popular # Hahtags

Popular Questions