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) About Me  (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) About Me  (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 aX%5E2%2BbX%2Bc=0 (in our case 6X%5E2%2B-13X%2B6+=+0) has the following solutons:

X%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-13%29%5E2-4%2A6%2A6=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+25+%29%29%2F2%5Ca.

X%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+1.5
X%5B2%5D+=+%28-%28-13%29-sqrt%28+25+%29%29%2F2%5C6+=+0.666666666666667

Quadratic expression 6X%5E2%2B-13X%2B6 can be factored:
6X%5E2%2B-13X%2B6+=+6%28X-1.5%29%2A%28X-0.666666666666667%29
Again, the answer is: 1.5, 0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-13%2Ax%2B6+%29

Answer by richwmiller(17219) About Me  (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