# Question #c3149

##### 2 Answers

#### Answer:

or

#### Explanation:

two consecutive odd integers

the sum is

product is

or

now we can solve for

for the final answer

so

a)

b)

both check so we are done

#### Answer:

or

#### Explanation:

Let's break this problem down:

We have two consecutive odd integers. How can we express that an two integers are odd and consecutive?

Imagine we had some integer

If

So, we can say that our two consecutive odd integers here are

Now, we need to set up an equation that represents the statement "their [the odd integers'] product is

Let's start with the integers product. Product means multiplication, so the product of our odd integers is just:

#(2n-1)(2n+1)#

However, this product is

#6[(2n-1)+(2n+1)]#

And since the product is

#(2n-1)(2n+1)=27+6[(2n-1)+(2n+1)]#

Now we can solve for

First, add

#(2n-1)(2n+1)=27+6(4n)#

#(2n-1)(2n+1)=27+24n#

Distribute (FOIL) on the left-hand side. Notice that since it is in the form

#4n^2-1=24n+27#

Move all the terms to the left-hand side:

#4n^2-24n-28=0#

Divide each term by

#n^2-6n-7=0#

To factor this, we're looking for two integers whose sum is

#(n-7)(n+1)=0#

Implying that:

#n=7# or#n=-1#

We'll take the positive solution of

If we wish to accept negative answers with