Opgave 2

\( \begin{array}{l} \left\{ \begin{array}{l} x^2 + xy = 20 \\ y^2 + xy = 30 \to x = \frac{{30 - y^2 }}{y} \\ \end{array} \right. \\ \downarrow \\ \left( {\frac{{30 - y^2 }}{y}} \right)^2 + \frac{{30 - y^2 }}{y} \cdot y = 20 \\ \frac{{30(30 - y^2 )}}{{y^2 }} = 20 \\ 900 - 30y^2 = 20y^2 \\ 50y^2 = 900 \\ y^2 = 45 \\ y = - 3\sqrt 2 \vee y = 3\sqrt 2 \\ \left\{ \begin{array}{l} x = - 2\sqrt 2 \\ y = - 3\sqrt 2 \\ \end{array} \right. \vee \left\{ \begin{array}{l} x = 2\sqrt 2 \\ y = 3\sqrt 2 \\ \end{array} \right. \\ xy = 12 \\ \end{array} \)