Math CentralQuandaries & Queries


Question from Chelsea, a student:

The sum of the squares of two consecutive negative even numbers is 100. Find the integers,

I'm really struggling with this problem and i've gotten to a point in the problem that I can't figure out what to do next.

Hi Chelsea,

An even integer can be written 2n for some integer n. The next even number is 2n + 2so the sum of the squares of two consecutive even numbers is

(2n)2 + (2n + 2)2

Hence you need to solve

(2n)2 + (2n + 2)2 = 100

You want negative even numbers so you need a negative value for n.

Expanding the equation above I get

4 n2 + 4 n2 + 8n + 4 = 100
8n2 + 8n + 4 = 100
4(2n2 + 2n + 1) = 100

Divide both sides by 4

2n2 + 2n + 1 = 25

Can you complete the problem now? Remember you want n to be negative. Make sure you verify your answer.


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