Q. 875.0( 1 Vote )

# The difference of the squares of two numbers is 45. The squaresÂ of thesmaller number is 4 times the larger number. DetermineÂ 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).

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