SOLUTION: The product of two consecutive odd integers is 1 less than four times their sum. Find the two integers.

Question 211832: The product of two consecutive odd integers is 1 less than four times their sum.
Find the two integers.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The product of two consecutive odd integers is 1 less than four times their sum.
Find the two integers.

Step 1. Let n be one odd integer.

Step 2. Let n+2 be the next consecutive odd integer.

Step 3. Translate problem statement into an equation such than n(n+2)=4(n+n+2)-1 since product is 1 less than four times their sum

where n(n+2) is the product of the two consecutive integers and (n+n+2) is the sum of the two integers

Step 4. Simplify to obtain a quadratic equation. Subtract 8n+7 from both sides of equation to get the right side of equation to be zero.

Step 5. Now we have a quadratic equation. So use quadratic formula given as

where

a=1, b=-6 and c=-7

The following steps solves the quadratic equation

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -1. Here's your graph:

Step 6. ANSWER: Based on the above steps, choose 7 since it is positive. The integers are then 7 and 9.

Step 7. Verify the answer using n(n+2)=4(n+n+2)+1 in Step 3.

So it checks out.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.

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