Question 1058011
Let x represent the first integer. The second integer is then represented by x - 3.


Since the sum of the squares is 269, you can write the following equation:


x^2 + (x - 3)^2 = 269


x^2 + x^2 - 6x + 9 = 269


2x^2 - 6x - 260 = 0


2(x^2 - 3x - 130) = 0


2(x - 13)(x + 10) = 0


x = 13, or x = -10


When x = 13, then the other number is 10.


When x = -10, then the other number is -13


Thus, there are two solutions:


1. 10 and 13

2. -10 and -13