SOLUTION: Help please! Is this solvable? The sum of a fraction and its reciprocal is 13/6. What is the fraction?

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Question 253272: Help please! Is this solvable?
The sum of a fraction and its reciprocal is 13/6. What is the fraction?
Found 3 solutions by drk, Greenfinch, richwmiller:
Answer by drk(1908)   (Show Source): You can put this solution on YOUR website!
Let x be the number.
x + 1/x = 13/6
multiply by x to get
x^2 + 1 = 13x/6
multiply by 6 to get
6x^2 -13x + 6 = 0
by quadratic, we get
x = 2/3.
2/3 + 3/2 = 13/6
Answer by Greenfinch(383)   (Show Source): You can put this solution on YOUR website!
Call the fraction X, the reciprocal is 1/X
So X + 1/x =13/6
Multiply by 6X to get 6x^2 +6 = 13X or
6x^2 - 13X +6
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=25 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.5, 0.666666666666667. Here's your graph:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
x+1/x=13/6
I will leave the details for you to enjoy.
x=2/3 and 3/2
check
3/2+2/3=13/6
9/6+4/6=13/6
13/6=13/6
ok
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