SOLUTION: the sum of the reciprocals of two consecutive intergers is 7/12 . find the two intergers

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Question 351022: the sum of the reciprocals of two consecutive intergers is 7/12 . find the two intergers
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers = x and x+1
1/x + 1/(x+1) = 7/12
12(x+1)+12x=7x(x+1) multiply each side by 12x(x+1).
12x+12+12x=7x^2+7x
7x^2-17x-12=0
x=3 quadratic equation. See below.
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B-17x%2B-12+=+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=%28-17%29%5E2-4%2A7%2A-12=625.

Discriminant d=625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17%2B-sqrt%28+625+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+625+%29%29%2F2%5C7+=+3
x%5B2%5D+=+%28-%28-17%29-sqrt%28+625+%29%29%2F2%5C7+=+-0.571428571428571

Quadratic expression 7x%5E2%2B-17x%2B-12 can be factored:
7x%5E2%2B-17x%2B-12+=+7%28x-3%29%2A%28x--0.571428571428571%29
Again, the answer is: 3, -0.571428571428571. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-17%2Ax%2B-12+%29