The sum of two positive numbers x and y (x y) is 50 and the difference of their squares is 720. Find the numbers.

Given, Sum of numbers = 50 ∴ x + y = 50 ⇒ x = 50 - y .........(1) Difference of squares = 720 ∴ x 2 - y 2 = 720 ⇒ (50 - y) 2 - y 2 = 720 ⇒ 50 2 + y 2 - 2 × 50 × y - y 2 = 720 ⇒ 2500 - 100y = 720 ⇒ 100y = 2500 - 720 ⇒ 100y = 1780 ⇒ y = = 17.80 Substituting value of y in equation (1), we get : ⇒ x = 50 - y = 50 - 17.80 = 32.20 Hence, numbers are 32.20 and 17.80