SOLUTION: the sum of a number and its reciprocal is 25\12 find the number

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Question 216454: the sum of a number and its reciprocal is 25\12 find the number
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
The sum of a number and its reciprocal is 25/12. Find the number

Step 1. Let x be the number and 1/x be its reciprocal.

Step 2. Then, since the sum of a number and its reciprocal is 25/12.

Step 3. Multiply 12x to both sides of the equation to get rid of the denominators.





Step 4. Subtract 25x to put the equation in quadratic form





Step 5. We can use the quadratic formula given as



where a=12, b=-25, and c=12.

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=49 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.33333333333333, 0.75. Here's your graph:



So or (reciprocals of each other)

Check... which is a true statement.

Step 6. ANSWER: The number is or which are reciprocals of each other

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.

Good luck in your studies!

Respectfully,
Dr J
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