SOLUTION: i want the value of x in (x+ 1/x)^2=3 and then show by submitting the x value in the equation

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Question 828975: i want the value of x in (x+ 1/x)^2=3 and then show by submitting the x value in the equation
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B+1%2Fx%29%5E2=3
take square root of each side
%28x%2B+1%2Fx%29=sqrt%283%29
multiply each side by x
%28x%5E2%2B+1%29=sqrt%283%29x
subtract sqrt(3)x from each side
x%5E2-sqrt%283%29x%2B1=0
Solutions are
x=%281%2F2%29%28sqrt%283%29-i%29 or x=%281%2F2%29%28sqrt%283%29%2Bi%29
See http://www.wolframalpha.com/input/?i=x^2-sqrt%283%29x%2B1%3D0
below is the solution by the solver
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1.73205080756888x%2B1+=+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=%28-1.73205080756888%29%5E2-4%2A1%2A1=-0.99999999999999.

The discriminant -0.99999999999999 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -0.99999999999999 is + or - sqrt%28+0.99999999999999%29+=+0.999999999999995.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1.73205080756888%2Ax%2B1+%29


Plugging solutions back into the equation will take some careful work.