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

Home > Just Math
Real Number Crossed Symmetric System of Equations (Posted on 2023-09-18) Difficulty: 3 of 5
Each of x, y, and z is a real number that satisfies this system of equations:
• 1/x+y+z=3
• x+1/y+z=3
• x+y+1/z=3
Determine all possible solutions to the above system of equations.

Note: Adapted from a problem that appeared on 2017 El Salvador Math Olympiad.

  Submitted by K Sengupta    
Rating: 5.0000 (1 votes)
Solution: (Hide)
The set of all solutions to the given system of equations is (x,y,z)={(1,1,1), (1/2,1/2,1/2), (3,3,-1/3), (3,-1/3,3), (-1/3,3,3)}.

For an explanation, refer to the solution submitted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionBrian Smith2023-09-18 11:06:10
SolutionsolutionLarry2023-09-18 09:58:32
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (2)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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