\left\{ \begin{array} { l } { \sqrt { 2 } b = \frac { - 1 + b ^ { 2 } + c ^ { 2 } } { c } } \\ { \sqrt { 1 - \frac { 1 } { 2 } b ^ { 2 } } + \frac { \sqrt { 2 } } { 2 } b = c } \end{array} \right.
Solve for b, c (complex solution)
b\neq -1
c=\frac{\sqrt{2}\left(\sqrt{2-b^{2}}+b\right)}{2}
Solve for b, c
b\in [-\sqrt{2},-1)\cup (-1,\sqrt{2}]\text{, }c=\frac{\sqrt{2}(\sqrt{2-b^{2}}+b)}{2}
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