TeX Quellcode:

\begin{array}{rclcl} -\dfrac{2(y-2)^2}{y}-2+\dfrac{(3y-8)^2}{3y} &=& \dfrac{14}{3y} &\vert& \cdot 3y \cr\cr -6(y-2)^2-6y+(3y-8)^2 &=& 14 &\vert& -14\cr -6y^2+24y-24-6y+9y^2-48y+64-14 &=& 0 \cr 3y^2-30y+26 &=& 0 &\vert& : 3 \cr y^2-10y+\dfrac{26}{3} &=& 0 &\vert& \text{p-q-Formel} \cr y_{1,2} &=& 5 \pm \sqrt{(-5)^2-\dfrac{26}{3}} \cr\cr y_{1,2} &=& 5 \pm \sqrt{\dfrac{49}{3}} \cr \cr\cr y_1 &=& 5+\dfrac{7}{\sqrt{3}} = 5+\dfrac{7\sqrt{3}}{3} \approx 9{,}04 \;\in\;\mathbb{D} \cr y_2 &=& 5-\dfrac{7}{\sqrt{3}} = 5-\dfrac{7\sqrt{3}}{3} \approx 0{,}96 \;\in\;\mathbb{D} \cr \cr \mathbb{L} &=& \left\{5+\dfrac{7\sqrt{3}}{3}; 5-\dfrac{7\sqrt{3}}{3}\right\} \end{array}