Math CentralQuandaries & Queries


Question from Terry, a student:

The product of two consecutive even integers is 14 more than their sum. Find the integers.

Hi Terry,

Since the smaller of the two integers is even it is divisible by 2 and hence it can be written 2n for some integer n. The next integer 2n + 1 is odd so the next even integer is 2n + 2.

What is the product of 2n and 2n + 2?

What is the sum of 2n and 2n + 2?

What is 14 more than this sum?

This is equal to their product and hence you have an equation you can solve for n.


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