OpenSAT

Let the two integers be x and y. We are given that xy = 48 and x - y = 2. Solving for x in the second equation gives us x = y + 2. Substituting y + 2 for x in the first equation gives (y + 2)y = 48, or y^2 + 2y = 48. Subtracting 48 from both sides yields y^2 + 2y - 48 = 0. Factoring this equation gives (y + 8)(y - 6) = 0, which means y = -8 or y = 6. Since the integers are positive, y must equal 6. Substituting 6 for y in the equation x = y + 2 gives us x = 6 + 2, or x = 8. Therefore, the sum of the two integers is 8 + 6 = 14.