The sum of the squares of two positive integers is 106 and the difference of the squares of the numbers is 56. Find the numbers.

Group of answer choices

x=56, y=52.7358

Step-by-step explanation:

x + y = 106

x = 106 - y

x^2 - y^2 = 56

(106 - y) ^2 - y^2 = 56

11236 - 212y + y^2 - y^2 = 56

11236 - 212y = 56

212y = 11236 - 56

212y = 11180

y = 52.7358

x = 106 - y = 106 - 52.7358 = 53.2642

(53.2642) ^2 - (52.7358) ^2 = 2837.08 - 2781.08 = 56