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
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