perplexus.info :: Just Math : Symmetry helps!

Symmetry helps! (Posted on 2016-10-26)

Solve the system of equations below, listing all un-ordered triplets of integers:

x^2 −(y+z+yz)x+ (y+z)yz = 0
y^2 −(z+x+zx)y+ (z+x)zx = 0
z^2 −(x+y+xy)z+ (x+y)xy = 0

See The Solution Submitted by Ady TZIDON

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

No Subject

| Comment 2 of 7 |

Solving the first quadratic equation shows the discriminant is the square of the coefficient of x, so x=1 or x=0.

By symmetry, those are the values of y and z as well.

Posted by xdog on 2016-10-26 23:03:01

Please log in:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info