SOLUTION: A number plus eight times its reciprocal is 6. Find the number?

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Question 952469: A number plus eight times its reciprocal is 6. Find the number?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
n=number
n%2B8%281%2Fn%29=6
n%2B%288%2Fn%29=6
%288%2Fn%29=6-n
8=6n-n%5E2
n%5E2-6n%2B8=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation an%5E2%2Bbn%2Bc=0 (in our case 1n%5E2%2B-6n%2B8+=+0) has the following solutons:

n%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=%28-6%29%5E2-4%2A1%2A8=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+4+%29%29%2F2%5Ca.

n%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+4
n%5B2%5D+=+%28-%28-6%29-sqrt%28+4+%29%29%2F2%5C1+=+2

Quadratic expression 1n%5E2%2B-6n%2B8 can be factored:
1n%5E2%2B-6n%2B8+=+1%28n-4%29%2A%28n-2%29
Again, the answer is: 4, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B8+%29

ANSWER: The number can be 2 or 4.
CHECK
For n=2
n+8(1/n)=6
2+8(1/2)=6
2+4=6
6=6
For n=4
n+8(1/n)=6
4+8(1/4)=6
4+2=6
6=6