SOLUTION: The sum of a number and its reciprocal is 1 3 _ 6 . Find the number

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Question 926556: The sum of a number and its reciprocal is 1 3
_
6
. Find
the number
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
let x be thew number
its reciprocal is 1/x
so +x%2B%281%2Fx%29=+13%2F6
L.C.M is x
so+%28+x%2Ax%2B1%29%2Fx++=13%2F6
+%28x%5E2%2B1%29%2Fx+=+13%2F6
multiply with 6 on both sides
%28x%5E2%2B1%29%2F%28x%29%2A6+=+%2813%2F6%29%2A6
%286x%5E2%2B6%29%2F%28x%29+=+13
multiply with x on both sides

%286x%5E2%2B6%29%2F%28x%29%2Ax+=+13%2Ax
%286x%5E2%2B6%29=+13%2Ax
6x%5E2-13x%2B6=0
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