I'm having difficulty determining a solution for (x + y) given the
two equations below:
c1 = 1/2*c2*(A*x^2 + B*y^2) and
A*x = B*y

All values are constants except for x & y.

Hi bravelobster-ga:

The answer to you question is:

(x+y) = +- (sqrt(2) * sqrt((c1*A)/(c2*B^2 + c2*B*A)) * (B+A)) / A

where

"+-" means plus or minus (i.e., two separate answers, one poisitive,
one negative)

"sqrt(   )" means the square root of the value in parenthases.

(I have attempted to attach a character-based rendering of this
solution to the end of this message, but I have no idea how it will
come through in the final posting.....)

How did I get the answer? I just happened to be working with Maple (a
symbolic algebra software package) at the time and was able to solve
it usign that.

You can find more information about Maple at:

http://www.maplesoft.com

If you need further clarification of the answer, please let me know. 

Thanks. 

websearcher-ga

character-based rendering:
                           1/2 /     c1 A     \1/2
                          2    |--------------|    (B + A)
                               |    2         |
                               \c2 B  + c2 B A/
                  x + y = --------------------------------    
                                      A

                           1/2 /     c1 A     \1/2
                          2    |--------------|    (B + A)
                               |    2         |
                               \c2 B  + c2 B A/
                  x + y = - --------------------------------
                                      A

A correct yet overly complex answer that needed to be simplified further.

I've come up with a solution in terms of y. I've verified this
solution by substituting numbers.

The solution is in graphic problem, as its easier to understand
compared to seeing text. Solution can be found at
http://scion.web1000.com/googlesol1.jpg

Websearcher's answer is correct, but the equation can be reduced
further to the form which can be seen in graphic form at
http://scion.web1000.com/googlesol2.jpg

Cheers,
aditya2k

Thank you 'aditya2k-ga' for reducing the answer given by
'websearcher-ga' to a simpler form.  I couldn't have done that myself.

1. c1 = half c2(Ax^2 + By^2)
2. Ax = By
from 2. 
=> Bxy = Ax^2 => x^2 = (B/A)xy
=> Axy = By^2 => y^2 = (A/B)xy
substitute in 1.
=> c1 = half c2(A + B)xy
xy = (2*c1) / (c2(A + B))
=> x^2 = 2*(B/A) * c1 / (c2(A + B))
=> y^2 = 2*(A/B) * c1 / (c2(A + B))
=> x+y = sqrt(2c1/c2) * sqrt((A+B)/AB)