SOLUTION: I have to find two numbers that equal 60 when multiplyed and equal 4 when added or subtracted. I can't find any though.

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Question 939478: I have to find two numbers that equal 60 when multiplyed and equal 4 when added or subtracted. I can't find any though.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I have to find two numbers that equal 60 when multiplyed and equal 4 when added or subtracted. I can't find any though.
============
x*y = 60
x - y = 4 --> y = x - 4
-----
Sub for y
x*(x-4) = 60
x^2 - 4x - 60 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-60+=+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=%28-4%29%5E2-4%2A1%2A-60=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+256+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+256+%29%29%2F2%5C1+=+10
x%5B2%5D+=+%28-%28-4%29-sqrt%28+256+%29%29%2F2%5C1+=+-6

Quadratic expression 1x%5E2%2B-4x%2B-60 can be factored:
1x%5E2%2B-4x%2B-60+=+%28x-10%29%2A%28x--6%29
Again, the answer is: 10, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-60+%29

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x = 6
y = 10
====================
x = -6
y = -10
====================
x*y = 60
x + y = 4 --> y = 4 - x
-----
Sub for y
x*(4 - x) = 60
-x^2 + 4x - 60 = 0
x^2 - 4x + 60 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B60+=+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=%28-4%29%5E2-4%2A1%2A60=-224.

The discriminant -224 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 -224 is + or - sqrt%28+224%29+=+14.9666295470958.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B60+%29

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x = 2 + sqrt(56)i, y = 2 - sqrt(56)i
x = 2 - sqrt(56)i, y = 2 + sqrt(56)i