SOLUTION: what is the product of two consecutive integers is 1 more than their sum. Find the integers?

Question 222965: what is the product of two consecutive integers is 1 more than their sum. Find the integers?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Consecutive integers are 1 apart from each other. So if one integer is "x" then the next one is "x+1". Now let's use these to translate
"the product of two consecutive integers is 1 more than their sum"

Product means multiplication so "the product of two consecutive integers" is (x)(x+1). Sum means addition so "their sum" is (x) + (x+1)

So "the product of two consecutive integers is 1 more than their sum" translates into:

Now we just need to solve this. Start by simplifying each side:

Next, since this is a quadratic equation (because of the ), we will get one side equal to zero by subtracting the entire right side from both sides:

Now we can solve this by factoring (or by using the quadratic formula):

The Zero Product Property tells us that if this or any product is equal to zero then one or more of the factors must be zero. So:
or
Solving each of these simple equations we get:
or
Now remember what "x" represents. (Look back at the beginning.) It represents the first (or smaller) of the two consecutive integers. And (x+1) represents the second (or larger) of the two. We have found two values for x: 2 and -1. So we have found two pairs of consecutive integers: