TeX Quellcode:

\begin{array}{rclll} \sqrt{p^2+1+3\sqrt{p-\dfrac{1}{2}}} &=& p+1 &\vert & ()^2 \\p^2+1+3\sqrt{p-\dfrac{1}{2}} &=& p^2+2p+1 &\vert & -p^2-1 \\3\sqrt{p-\dfrac{1}{2}} &=& 2p &\vert& :3 \\\sqrt{p-\dfrac{1}{2}} &=& \dfrac{2p}{3} &\vert & ()^2 \\p-\dfrac{1}{2} &=& \dfrac{4p^2}{9} &\vert & -\dfrac{4p^2}{9} \\-\dfrac{4}{9}p^2+p-\dfrac{1}{2} &=& 0 &\vert & :\left(-\dfrac{4}{9}\right) \\p^2-\dfrac{9}{4}+\dfrac{9}{8} &=& 0 &\vert & \text{p-q-Formel} \\p_{1,2} &=& \dfrac{9}{8}\pm\sqrt{\left(-\dfrac{9}{8}\right)^2-\dfrac{9}{8}} \\p_{1,2} &=& \dfrac{9}{8}\pm\sqrt{\dfrac{9}{64}} \\\\p_{1} &=& \dfrac{9}{8}+\dfrac{3}{8} = \dfrac{3}{2} \in\mathbb{D} \\\\p_{2} &=& \dfrac{9}{8}\pm\dfrac{3}{8} = \dfrac{3}{4} \in\mathbb{D}\end{array}