To make the writing much easier, let
`R_1^2=X` `R_2^2=Y` `r_1^2=x` `r_2^2=y`
So the equation becomes:
`kC=sqrt(X-Y)+sqrt(x-y)-A`, and we now need to solve for x.
Add A to both sides; subtract `sqrt(X-Y)` from both sides:
and then square both sides:
We now re-express it in the original notation:
We have solved the equation for `r_1^2`, as required. There is no need to expand out the last bracket on the RHS.