OK, working this out:

\(\displaystyle A = (A_{x} + A_{y})^{1/2}\)

\(\displaystyle A^{2} = ((A_{x} + A_{y})^{1/2})^{2}\)

\(\displaystyle A^{2} = A_{x} + A_{y}\)

\(\displaystyle 0 = A_{x} + A_{y} - A^{2}\)

\(\displaystyle -A_{x} = A_{y} - A^{2}\)

\(\displaystyle A_{x} = -A_{y} + A^{2}\)

rewritten

\(\displaystyle A_{x} = A^{2} - A_{y}\)