SOLUTION: " What is the number if a number is added to its reciprocal the sum is 25/12?"

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Question 389550: " What is the number if a number is added to its reciprocal the sum is 25/12?"
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x + (1/x) = 25/12
x%5E2+%2B+1+=+25x%2F12
12x%5E2+-+25x+%2B+12+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B-25x%2B12+=+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=%28-25%29%5E2-4%2A12%2A12=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--25%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+49+%29%29%2F2%5C12+=+1.33333333333333
x%5B2%5D+=+%28-%28-25%29-sqrt%28+49+%29%29%2F2%5C12+=+0.75

Quadratic expression 12x%5E2%2B-25x%2B12 can be factored:
12x%5E2%2B-25x%2B12+=+%28x-1.33333333333333%29%2A%28x-0.75%29
Again, the answer is: 1.33333333333333, 0.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-25%2Ax%2B12+%29

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x = 3/4
x = 4/3