SOLUTION: Find 2 numbers m and n whose sum is 10 and whose product is 18.

Question 227053: Find 2 numbers m and n whose sum is 10 and whose product is 18.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Find 2 numbers m and n whose sum is 10 and whose product is 18.

Step 1. Let m+n=10 since the sum is 10.

Step 2. Let mn=18 since the product is 18.

Step 3. Then m=10-n and n(10-n)=18. Subtract 18 from both sides of the equation leads to

Step 4. To solve use the quadratic equation given as

where a=1, b=-10, and c=18.

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=28 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.64575131106459, 2.35424868893541. Here's your graph:

Note the above solutions in n are the numbers whose sum is 10 and product is 18.

Step 5. ANSWER: Then numbers are approximately 2.35 and 7.65.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

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