The product of two consecutive positive even integers is 12,320. What are the two integers?

Question

mathmate · Answer

x(x+2)=12320
you can solve for x by factoring.

mathmate · Answer

For problems like this, take sqrt(12320) and it would be close to the answer you need.

mathmate · Answer

Add 1 and subtract 1 to get the two positive integers, no need to solve quadratic equations!

anonymous · Answer

would I just divide the product by 2?

mathmate · Answer

Dividing 12320 would suit the requirement "two consecutive even numbers ADD to 12320".
Since they multiply to get 12320, the square root is an approximation of the average (111) of the two even integers (110 and 112).

mathmate · Answer

Of course, mathematically we're supposed to solve the quadratic equation.

anonymous · Answer

so are those last two numbers the two integers we're looking for?

mathmate · Answer

Yes, 110 is also the solution to the quadratic equation.  You'd have to add to to get the other integer, which makes 112.

anonymous · Answer

thanks!

mathmate · Answer

"two"  (erratum)

You're welcome!  :)