SOLUTION: The product of two consecutive even integers is 288. find the integers

Question 100405: The product of two consecutive even integers is 288. find the integers
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Consecutive even integers follow the form: , , , ...., etc.

So the product of two consecutive even integers is:

Distribute

Subtract 288 from both sides

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=4, b=4, and c=-288

Square 4 to get 16

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 4 to get 8

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Now plug in to find the two numbers

So one pair of numbers is 16 and 18

Now plug in to find the two numbers

So another pair of numbers is -18 and -16
RELATED QUESTIONS
Find the product of two consecutive positive even integers is 288. Find the... (answered by Alan3354)

The product of two consecutive even integers is 288. find the... (answered by tutor_paul)

the product of two consecutive positive even integers is 288. Find the... (answered by malakumar_kos@yahoo.com)

The product of two consecutive positive even integers is 288 find the... (answered by ankor@dixie-net.com)

find two consecutive even integers whose product is... (answered by kirubakaran)

find two consecutive even integers whose product is... (answered by jim_thompson5910)

the product of two consecutive positive integers is 288. Find the... (answered by venugopalramana)

The product of two consecutive positive even integers is 288. Find the two integers.... (answered by Alan3354)

I am having some problems with this problems The product of two consecutive postive... (answered by Earlsdon)