The larger of two integers is two less than 3/2 of the smaller. The sum of the squares of these two numbers is 269. Find these two integers.

Question

solve and write equation

Answer 1

Let x = the smaller integer

Let (3/2)x - 2 = the larger integer

x² + [(3/2)x - 2]² = 269

x² + (9/4)x² - 6x  4 = 269

(13/4)x² -6x - 265 = 0       Multiply both sides by 4.

13x² - 24x - 1060 = 0

(13x + 106)(x - 10) = 0

12x + 106 = 0       or      x - 10 = 0

12 x = -106    or    x = 10

x = 8.833, not an integer

x = 10

(3/2)(10) - 2 = 13