algebra word pronblem

Question

the difference between 2 positive integers is 3.  If the smaller is added to the square of the larger, the sum is 339.  find the integers.

Answer 1

Let x and y be the two unknowns positive integers

• the difference between 2 positive integers is 3:  x - y = 3
• If the smaller is added to the square of the larger, the sum is 339:  x² + y = 339

 

Since x-y = 3, then x = y+3.  Substitute y+3 in place of x in the second equation.

 

      x² + y = 339

      (y+3)² + y = 339

      y² + 6y + 9 + y = 330

      y² + 7y - 330 = 0

 

Factors to:

 

      (y+22)(y-15) = 0

 

y = -22 and 15.  Since we want positive integers, y = 15.  x = y+3 = 18.

 

Check:

      18²+15 = 339

      324+15 = 339

      339 = 339

      Check!