The sum of the squares two consecutive even numbers minus the square of the next odd number is 105. Write an algebraic equation that can be used to solve this problem. What is the larger even number?

Question

Not understanding how to do this specific problem.

Answer 1

I have a problem with this problem!

Let 2n and 2n+2 be the 2 consecutive even numbers, then 2n+3 is the next odd number.

This gives the following equation: (2n)² + (2n+2)² - (2n+3)² = 105

When you expand and then collect these terms you get:

4n² - 4n - 110 = 0 => 2n² - 2n - 55 = 0 which has NO integer solutions!

If you can point out a flaw in my solution, please do; otherwise, I think there is an error in the staement of the problem.