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

Let the larger number be x . Given, the square of the smaller number is 4 times the larger number. Hence, square of smaller number = 4x Given, the difference of squares of two numbers is = 45 If x = -5 , , which is not valid as there is no real value of square root of a negative value. ∴ x = 9 , . Hence, the two numbers are 9, 6 or 9, -6.