The difference between two positive integers is 3. If the smaller is added to the square of the larger, the sum is 417. Find the integers

Answer 1

smaller --- x
larger --- x+3

(x+3)^2 + x = 417
x^2 + 6x + 9 + x - 417 = 0
x^2 + 7x - 408 = 0

factor, then solve for x, reject the negative value for x

Answer 2

let x = smaller , y = larger

y - x = 3 ... y - 3 = x

y^2 + x = 417

solve the system