While working on an engineering problem, we have met a non linear system of two variables and two equations.
$$ \left\{ \begin{array}{c} A=x \sin y \\ B=-x^2 + x \cos y \end{array} \right. $$ where $A$ and $B$ are constants.
if the system is solved analytically two solutions ($Z1$ and $Z2$) can be found from: $(A^2+B^2)+Z^2+Z(2B -1) =0 $
where $Z=x^2$
but if we solve the system with Newton-Raphson method only one solution is found. How to obtain the second one?