# math

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the product of two even consecutive integers is 224. find the integers

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14 and 16.

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how do u figure that out?

• math -

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.

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