SOLUTION: Hi, I need a full calculation on this: a+b+15=36 ^ A^2+b^2=15 I know the answer but I have no idea how to put this in calculation, please me :)

Algebra ->  Pythagorean-theorem -> SOLUTION: Hi, I need a full calculation on this: a+b+15=36 ^ A^2+b^2=15 I know the answer but I have no idea how to put this in calculation, please me :)      Log On


   

Question 975930: Hi, I need a full calculation on this:
a+b+15=36 ^ A^2+b^2=15
I know the answer but I have no idea how to put this in calculation, please me :)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If you mean:
a+b+15=36
a^2+b^2=15
------------
a + b = 21 --> b = 21-a
a^2 + b^2 = 21
Sub for b
a%5E2+%2B+%2821-a%29%5E2+=+21
2a%5E2+-+42a+%2B+420+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-42x%2B420+=+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=%28-42%29%5E2-4%2A2%2A420=-1596.

The discriminant -1596 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 -1596 is + or - sqrt%28+1596%29+=+39.9499687108764.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-42%2Ax%2B420+%29

=================
a+=+21%2F2+%2B-sqrt%28-1596%29%2F4
a+=+21%2F2+%2B-i%2Asqrt%28399%29%2F2
----------------------
b = conjugate of a