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Symmetry helps! (Posted on 2016-10-26) Difficulty: 4 of 5
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    
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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
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