Inequalities

Art of Problem Solving

AoPS Online

High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

3 M G

BBookmark VNew Topic kLocked

High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

3 M G

BBookmark VNew Topic kLocked

No tags match your search

M

Inequalities

G H J

Reveal topic tags

L

G H BBookmark kLocked kLocked NReply

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

42617 posts

sqing

#1 h Apr 27, 2025, 2:59 PM

Y by

Let $x, y \geq \frac{3}{2}$ . Prove that
$\frac{2}{1+xy} + x + y \geq \frac{x}{y} + \frac{y}{x}+ \frac{21}{13}$ Let $x, y \geq 2$ . Prove that
$\frac{2}{1+xy} + x + y \geq \frac{x}{y} + \frac{y}{x}+ \frac{12}{5}$ Let $0< x, y \leq \frac{3}{2}$ . Prove that
$\frac{2}{1+xy} + x + y \leq \frac{x}{y} + \frac{y}{x}+\frac{21}{13}$ Let $0< x, y \leq 2$ . Prove that
$\frac{2}{1+xy} + x + y \leq \frac{x}{y} + \frac{y}{x}+\frac{12}{5}$

This post has been edited 1 time. Last edited by sqing, Apr 27, 2025, 3:17 PM

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

1720 posts

DAVROS

#2 h Apr 28, 2025, 7:50 AM

Y by

sqing wrote:

Let $x, y \geq 2$ . Prove that $\frac{2}{1+xy} + x + y \geq \frac{x}{y} + \frac{y}{x}+ \frac{12}{5}$

solution

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

42617 posts

sqing

#3 h Apr 28, 2025, 8:24 AM

Y by

Very very nice.Thank DAVROS.

Z K Y

N Quick Reply

G

H

=

© 2025 AoPS Incorporated

a