SOLUTION: Find a number such that subtracting its reciprocal from the number gives 16/15.

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Question 22579: Find a number such that subtracting its reciprocal from the number gives 16/15.
Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be "x".
EQUATION:
x-(1/x) = 16/15
Multiply both sides by 15x to get:
15x^2-15=16x
15x^2-16x-16=0
Using the quadratic formula you get x=5/3
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 15x%5E2%2B-16x%2B-15+=+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%2A15%2A-15=1156.

Discriminant d=1156 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+1156+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+1156+%29%29%2F2%5C15+=+1.66666666666667
x%5B2%5D+=+%28-%28-16%29-sqrt%28+1156+%29%29%2F2%5C15+=+-0.6

Quadratic expression 15x%5E2%2B-16x%2B-15 can be factored:
15x%5E2%2B-16x%2B-15+=+15%28x-1.66666666666667%29%2A%28x--0.6%29
Again, the answer is: 1.66666666666667, -0.6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-16%2Ax%2B-15+%29

Cheers,
Stan H.