Question

find two positive integers whose product is 24,999,999 and whose positive difference is as small as possible. explain how you discovered them

Answer 1

5001 and 4999

Explanation:

25,000,000 is the square of 5,000 and 24,999,999 is one less than it. Notice that the situation resembles the expression
`x^2-1` in which x would be 5,000.

`x^2-1` can be factored into
`(x+1)(x-1)`, and substituting x with 5000 yields:
`(5000+1)(5000-1)`. This can also be written as
`(5001)(4999)`. Therefore, the integers would be 5001 and 4999.