Question

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

Answer 1

Let the two positive numbers be a and b.
Given difference between them is 5 and sum of squares is 73.

So a - b = 5, a² + b² = 73
Squaring on both sides gives
(a - b)² = 5²
a² + b² - 2ab = 25
but a² + b² = 73
so 2ab = 73 - 25 = 48
ab = 24
So, the product of numbers is 24.