posted by Cho .
the product of two even consecutive integers is 224. find the integers
14 and 16.
how do u figure that out?
Just try them quickly, there's a more formal method, but it'd be much more complicated for such a simple problem.
They want only even numbers. You can quickly see 10 x 12 = 120 is smaller than 224 and 18 x 20 = 360 is too big.
You're left with 12 x 14, 14 x 16, etc. Turns out 14 x 16 works.
Anyway, here's the formal method :
Let "Y" be an even number.
We want Y x (Y+2)= 224
We get Y^2 +2y -224=0
And the solution for this equation is Y=14. So the answer is Y and Y+2, 14 and 16.