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

Question: The product of two numbers is 120 and the sum of their square is 289. The sum of the numbers is:

Solution:
Let the numbers be x and y
Then,
xy = 120
and x² + y² = 289

∴ (x + y)²
= x² + y² + 2xy = 289 + 240 = 529 [2xy = 2 × 120 = 240]

∴ x + y = √529 = 23