Two positive numbers have a difference of 4 and a product of 96. What are the numbers?

Hello:

the numbers are : x, y

x - y = 4 ... 1)

xy = 96 ... (2)

by (1) : x = y + 4 ... (*)

subsct in (2) : (y+4) y = 96

y² + 4y - 96 = 0

(y² + 2 (2y) + 2²) - 2² - 96 = 0

(y+2) ² - 100 = 0

(y+2) ² = 10²

y + 2 = 10 or y+2 = - 10

y = 8 or y = - 12 (refused : x is positif)

y = 8

subsct in (*) : x = 8+4 = 12

the numbers are : 12 and 8

12-8 = 4 and 12*8 = 96