SOLUTION: 1/x + 1/(x+1) = 15/56

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Question 407624: 1/x + 1/(x+1) = 15/56
Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
1/x + 1/(x+1) = 15/56
multiply both sides by (x)*(x+1) and get
1/x*(x*(x+1)) + (1/(x+1))*(x*(x+1)) = (15/56)*(x*(x+1))
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(x+1) + x = (15/56)*(x^2 + x)
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2*x + 1 = (15/56)*x^2 +(15/56)*x
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-0.2678*x^2 -0.2678*x +2*x +1 = 0
-0.2678*x^2 + 1.7321*x + 1 = 0


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.2678x%5E2%2B1.7321x%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=%281.7321%29%5E2-4%2A-0.2678%2A1=4.07137041.

Discriminant d=4.07137041 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1.7321%2B-sqrt%28+4.07137041+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281.7321%29%2Bsqrt%28+4.07137041+%29%29%2F2%5C-0.2678+=+-0.533352716778202
x%5B2%5D+=+%28-%281.7321%29-sqrt%28+4.07137041+%29%29%2F2%5C-0.2678+=+7.00123919922779

Quadratic expression -0.2678x%5E2%2B1.7321x%2B1 can be factored:
-0.2678x%5E2%2B1.7321x%2B1+=+-0.2678%28x--0.533352716778202%29%2A%28x-7.00123919922779%29
Again, the answer is: -0.533352716778202, 7.00123919922779. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.2678%2Ax%5E2%2B1.7321%2Ax%2B1+%29