SOLUTION: {{{x + 1/3x = 8}}}

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Question 451218: x+%2B+1%2F3x+=+8
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
x+1/3x=8
3x2+1=24x
3x2-24x+1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-24x%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=%28-24%29%5E2-4%2A3%2A1=564.

Discriminant d=564 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--24%2B-sqrt%28+564+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+564+%29%29%2F2%5C3+=+7.95811402901264
x%5B2%5D+=+%28-%28-24%29-sqrt%28+564+%29%29%2F2%5C3+=+0.0418859709873611

Quadratic expression 3x%5E2%2B-24x%2B1 can be factored:
3x%5E2%2B-24x%2B1+=+3%28x-7.95811402901264%29%2A%28x-0.0418859709873611%29
Again, the answer is: 7.95811402901264, 0.0418859709873611. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-24%2Ax%2B1+%29