SOLUTION: A sum of a number and 7 times it's reciprocal is (16/3). Please solve for the number.

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Question 168656: A sum of a number and 7 times it's reciprocal is (16/3). Please solve for the number.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the number x
so x+7(1/x)=16/3---> multiply all terms by 3x
:
3x^2+21=16x
:
3x%5E2-16x%2B21=0
x=3 and 2.333(7/3)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-16x%2B21+=+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=%28-16%29%5E2-4%2A3%2A21=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+4+%29%29%2F2%5C3+=+3
x%5B2%5D+=+%28-%28-16%29-sqrt%28+4+%29%29%2F2%5C3+=+2.33333333333333

Quadratic expression 3x%5E2%2B-16x%2B21 can be factored:
3x%5E2%2B-16x%2B21+=+3%28x-3%29%2A%28x-2.33333333333333%29
Again, the answer is: 3, 2.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-16%2Ax%2B21+%29