The difference of the squares of two numbers is 45. The squares of thesmaller number is 4 times the larger number. Determine the numbers.

Let one number be x.
Then the other number is (x ² - 45).
Condition: The squares of the smaller number is 4 times the larger number.
(x ² – 45) = 4x
x ² – 4x – 45 = 0
x ² – 9x + 5x – 45 = 0
x(x – 9) + 5(x – 9) = 0
(x + 5)(x – 9) = 0
(x + 5) = 0 or (x – 9) = 0
x = –5 or x = 9
Therefore the numbers are 9 and

Checking:
6 ² = 36 = 4(9).