SOLUTION: Help? Im kinda confused on this one: Find three consecutive integers such that the product of the first and the third is 20 more than the second.(Application of Quadratic function

Question 893361: Help? Im kinda confused on this one:
Find three consecutive integers such that the product of the first and the third is 20 more than the second.(Application of Quadratic function.)
I've tried with
xz=y+20
or
(a sub 1)(a sub 3)= (a sub 2)+ 20
but cant derive any equations for the three variables
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Consecutive Integers x, x+1, x+2.

The description, .
Simplify.

Will x really be an integer?

Discriminant: . This is not a square.
The quadratic expression cannot be factored to have integer coefficients.
The numbers WILL NOT be integers.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x^2+2x-21=0

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :

1,3,7,21

-1,-3,-7,-21

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .

1*(-21) = -21
3*(-7) = -21
(-1)*(21) = -21
(-3)*(7) = -21

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number Second Number Sum
1 -21 1+(-21)=-20
3 -7 3+(-7)=-4
-1 21 -1+21=20
-3 7 -3+7=4

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

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