Quadratic equations

Question

find two rational number which differ by 3 and the sum of whose squares is 117.

Answer 1

The 2 numbers are x and x +3.

x² + (x + 3)² = 117

2x² + 6x + 9 = 117

2x² + 6x - 108 = 0

x² + 3x - 54 = 0

(x - 6)(x + 9) = 0

There are 2 sets pf numbers:

6 and 9

-9 and -6

Test the answers.