Question #c3149
2 Answers
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
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