SOLUTION: Find 2 fractions whose product is 3/32 and whose sum is 7/8.

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Question 271534: Find 2 fractions whose product is 3/32 and whose sum is 7/8.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let the fractions be x & y
xy=3/32
x+y=7/8
.
y=(7/8)-x
x((7/8)-x)=3/32 substitute (7/8)-x for y.
32x((7/8)-x)=3
28x-32x^2=3
32x^2-28x+3=0
x=3/4, y=1/8 or vice versa
.
Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 32x%5E2%2B-28x%2B3+=+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=%28-28%29%5E2-4%2A32%2A3=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--28%2B-sqrt%28+400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-28%29%2Bsqrt%28+400+%29%29%2F2%5C32+=+0.75
x%5B2%5D+=+%28-%28-28%29-sqrt%28+400+%29%29%2F2%5C32+=+0.125

Quadratic expression 32x%5E2%2B-28x%2B3 can be factored:
32x%5E2%2B-28x%2B3+=+32%28x-0.75%29%2A%28x-0.125%29
Again, the answer is: 0.75, 0.125. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+32%2Ax%5E2%2B-28%2Ax%2B3+%29