77.4k views
1 vote
find two positive integers whose product is 24,999,999 and whose positive difference is as small as possible. explain how you discovered them

User Shavit
by
7.1k points

1 Answer

6 votes

Answer:

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.

User Dima Lituiev
by
7.5k points