SOLUTION: The sum of a number and its reciprocal is 85/42. Find the number.

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Question 541670: The sum of a number and its reciprocal is 85/42. Find the number.
Answer by neatmath(302)   (Show Source): You can put this solution on YOUR website!

Let's first set up an equation using x as our variable:



Then we just need to solve for x:









Then we can use the quadratic formula to solve for x:

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=169 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.16666666666667, 0.857142857142857. Here's your graph:


This gives us a good approximation to work with.

Using an online factoring calculator, we find that our equation factors as:



From this we can easily see that or

It would take us a BIT of time to factor that equation properly and get the exact answer.

I'm trying to think of other ways off the top of my head to solve this.

I hope this helps!
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