Question 1052208
larger integer = x
smaller integer = y


x = 2y - 3
x^2 + y^2 = 117


Use substitution. 


(2y - 3)^2 + y^2 = 117
4y^2 - 12y + 9 + y^2 = 117
5y^2 - 12y - 108 = 0
(y - 6)(5y + 18) = 0


y is an integer, so y = 6.


The integers are x = 9 and y = 6.