All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Three numbers (Posted on 2003-11-17) Difficulty: 3 of 5
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have ?

No Solution Yet Submitted by Ravi Raja    
Rating: 3.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: solution - corrected, I think | Comment 8 of 22 |
(In reply to solution by Charlie)

It's a good thought, and Charlie made an algebraic mistake (I think).

It *can* be simplified to -y² + (5-x)y + 5x - x² - 3 = 0 (He forgot the -3).

Continue with this... find the descriminant, and I think you'll find the bounds to be 5/3 ± 8/3. And the higher of the two is 13/3, which agrees with what I wrote earlier.

--- SK
Edited on November 17, 2003, 5:18 pm
  Posted by SilverKnight on 2003-11-17 17:17:00

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information