Question

The difference of the squares of two positive integers is 180. The square of the smaller number is 8 times the larger, find the numbers.

Answer 1

Let the larger number = x
Then the square of the smaller number = 8 times the larger number = 8x
and the square of the larger number=
According to the question,


Thus the larger number = 18 or -10.
Then, the square of the smaller number =

But the square of a number can not be negative so the square of smaller number is 144.
Hence the smaller number is
Therefore the numbers are 12 and 18.