i need help with this question

Question

you have two positive numbers.The second number is two more than the first number.The difference of their squares is 24.Find both positive numbers.

Answer 1

Assume X a positive number, the 2nd number Y = X + 2, since Y > X then the difference of the two squares is

Y² - X² = 24, then ( X +2)² - X² = 24, expand the equation, X² + 4X+4 - X² = 24 remove paranthesis

and 4X +4 = 24, add -4 to both sides, 4X +4 - 4 = 24 - 4, 4X = 20, divide by 4 on both sides ( 4X/4) = ( 20/4) , and X = 5, and Y = 5+2 = 7 , Verify that Y² - X² = 24

( 7)² - ( 5)² = 49 - 25 = 24, the solution checks X = 5, and Y = 7