The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the… · ABC26GN1709

Let the numbers be x and (x + 3). Then, x2 + (x + 3)2 = 369 ⇔ x2 + x2 + 9 + 6x = 369 ⇔ 2x2 + 6x – 360 = 0 ⇔ x2 + 3x – 180 = 0 ⇔ (x + 15) (x – 12) = 0 ⇔ x = 12. So, the numbers are 12 and 15. \ Required sum = (12 + 15) = 27.