SOLUTION: Solve and check. x-1/x^2+4 = 1.

Algebra ->  Equations -> SOLUTION: Solve and check. x-1/x^2+4 = 1.      Log On


   

Question 247187: Solve and check.
x-1/x^2+4 = 1.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x-1/x^2+4 = 1
x-1=x^2+4
x^2-x+5=0 Subtract the left side from the right.
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B5+=+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%29%5E2-4%2A1%2A5=-19.

The discriminant -19 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 -19 is + or - sqrt%28+19%29+=+4.35889894354067.

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%2Ax%2B5+%29