Opgave 1

\( \begin{array}{l} \left\{ \begin{array}{l} a + b = 2ab \\ b + c = 3bc \\ a + c = 7ac \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{1}{b} + \frac{1}{a} = 2 \\ \frac{1}{c} + \frac{1}{b} = 3 \\ \frac{1}{c} + \frac{1}{a} = 7 \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{1}{b} + \frac{1}{a} = 2 \\ \frac{1}{c} - \frac{1}{a} = 1 \\ \frac{1}{c} + \frac{1}{a} = 7 \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{1}{b} + \frac{1}{a} = 2 \\ \frac{1}{c} - \frac{1}{a} = 1 \\ \frac{2}{c} = 8 \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{1}{b} + \frac{1}{a} = 2 \\ \frac{1}{c} - \frac{1}{a} = 1 \\ c = \frac{1}{4} \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{1}{b} + \frac{1}{a} = 2 \\ 4 - \frac{1}{a} = 1 \\ c = \frac{1}{4} \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{1}{b} + \frac{1}{a} = 2 \\ a = \frac{1}{3} \\ c = \frac{1}{4} \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{1}{b} + 3 = 2 \\ a = \frac{1}{3} \\ c = \frac{1}{4} \\ \end{array} \right. \\ \left\{ \begin{array}{l} b = - 1 \\ a = \frac{1}{3} \\ c = \frac{1}{4} \\ \end{array} \right. \\ \end{array} \)