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.

Answer

9 and 6

Explanation

Let the required natural numbers be a and b. Then,
`(a^(2)-b^(2)=45" and "b^(2)=4a)implies(a^(2)-4a-45)=0.`