The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:Solution: let the two numbers be x, y xy = 120 x2 + y2 = 289 We know(x + y)2 = x2 + y2 + 2xy⇒ (x + y)2 = 289 + 2 × 120 ⇒ (x + y)2 = 289 + 240⇒ (x + y)2 = 529⇒ (x + y)2 = 232∴ x + y = 23