SOLUTION: The difference between two whole numbers is 8 and the difference between their reciprocals is 1/6. Find the two numbers.

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Question 60964This question is from textbook Algebra for College Students
: The difference between two whole numbers is 8 and the difference between their reciprocals is 1/6. Find the two numbers. This question is from textbook Algebra for College Students

Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between two whole numbers is 8 ==> Eq. 1: X-Y=8
The difference between their reciprocals is 1/6 ==> Eq. 2: 1%2FX-1%2FY=1%2F6
Eq.1==>X=Y%2B8
plug into Eq. 2: 1%2F%28Y%2B8%29-1%2FY=1%2F6
%28Y-%28Y%2B8%29%29%2FY%28Y%2B8%29=1%2F6
-8%2A6=Y%5E2%2B8%2AY
Y%5E2%2B8Y%2B48=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aY%5E2%2BbY%2Bc=0 (in our case 1Y%5E2%2B8Y%2B48+=+0) has the following solutons:

Y%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=%288%29%5E2-4%2A1%2A48=-128.

The discriminant -128 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -128 is + or - sqrt%28+128%29+=+11.3137084989848.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B48+%29