Find all sets of integers {x,y,z} such that when any one of these numbers is added to the product of the other two numbers, the result is always 2.

Answer 1

There are only two such triplets

(1,1,1) because 1 + 1*1 = 2
(-2,-2,-2) because -2 + (-2)(-2) = 2

( I sort of cheated, I made myself up a small BASIC computer program)

Answer 2

thanks(:

is there any reason why those are the answers? like is there any pattern in finding them?