SOLUTION: the sum of two numbers is 35 and their product is 7. find the sum of the reciprocals of the numbers.

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Question 245478: the sum of two numbers is 35 and their product is 7. find the sum of the reciprocals of the numbers.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a+b=35
a*b=7
a=35-b
(35-b)*b=7
35b-b^2=7
0=b^2-35b+7
there is something wrong with the graph
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-35x%2B7+=+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=%28-35%29%5E2-4%2A1%2A7=1197.

Discriminant d=1197 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--35%2B-sqrt%28+1197+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+1197+%29%29%2F2%5C1+=+34.7988438920062
x%5B2%5D+=+%28-%28-35%29-sqrt%28+1197+%29%29%2F2%5C1+=+0.201156107993807

Quadratic expression 1x%5E2%2B-35x%2B7 can be factored:
1x%5E2%2B-35x%2B7+=+1%28x-34.7988438920062%29%2A%28x-0.201156107993807%29
Again, the answer is: 34.7988438920062, 0.201156107993807. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-35%2Ax%2B7+%29