SOLUTION: The question is: Find two positive integers tha differ by 4 and whose product is 221. I know the answer is 13 and 17, but would like to know how to arrive at that algebraicly.

Question 211955: The question is:
Find two positive integers tha differ by 4 and whose product is 221. I know the answer is 13 and 17, but would like to know how to arrive at that algebraicly.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The question is:

Find two positive integers that differ by 4 and whose product is 221. I know the answer is 13 and 17, but would like to know how to arrive at that algebraically.

Step 1. Two Positive Integers that differ by 4. Say n is one positive integer. Since the two numbers differ by 4, then the other must can be either n+4 or n-4. We'll choose n+4 but you can use n-4 and get similar results.

Step 2. Product is 221. This means that n(n+4)=221.

Step 3. Multiply the equation is step 2. . This will reduce to a quadratic equation given as

where we subtracted 221 from both sides of the equation in the first equation of Step 3.

Step 4. Now follow the process of solving a quadratic equation

where a=1, b=4 and c=-221

The steps are shown below. The solutions to the quadratic equation equation below are 13 and -17 and will intercept the x-axis in the parabola such that y=0. However, please ignore the graph for the moment since solution exceeded the limits for the graph.

Step 4a. Since we want a positive numbers then choose n=13. Therefore n+4=17.

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=900 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 13, -17. Here's your graph:

For step-by-step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.Tv/courses/IntroAlgebra

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