The product of the positive integers is equal to twice their sum. This product is also equal to six times the difference between the two integers. What is the sum of these two integers

x + y = 9.

Step-by-step explanation:

xy = 2 (x + y)

xy = 6 (x - y)

2x + 2y = 6x - 6y

8y = 4x

x = 2y

Substitute for x in the first equation:

2y^2 = 2 (2y + y)

2y^2 = 6y

y^2 = 3y

y (y - 3) = 0

y = 0, 3.

x = 2y = 0, 6.

As the integers are positive they must be 3 and 6.

x + y = 3+6 = 9.