perplexus.info :: Just Math : Real Number Crossed Symmetric System of Equations

Real Number Crossed Symmetric System of Equations (Posted on 2023-09-18)

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
Solution	Brian Smith	2023-09-18 11:06:10
solution	Larry	2023-09-18 09:58:32

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