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

(In reply to

re: my short solution by Daniel)

You are right.

No need to show it 3 times (one quotes 0! - don't know why)

for (x,y,z)=(-1,1,1) lhs =1^2-(-1-1+1)+(-2*1)=1+1-2

SYMMETRY HELPS, so we add 2 additional triplets: (1,-1,1) AND (1,1,-1)

summing up: (0,0,0), (1,1,1,), (-1,1,1,), (1,-1,1,), (1,1,-1,).