TeX Quellcode:
\begin{array}{rclll} \sqrt{t+\sqrt{2t+5}} &=& \sqrt{3t+1} &\vert & ()^2\\t+\sqrt{2t+5} &=& 3t+1 &\vert & -t \\\sqrt{2t+5} &=& 2t+1 &\vert & ()^2\\2t+5 &=& 4t^2+4t+1 &\vert & -4t^2-4t-1\\-4t^2-2t+4 &=& 0 &\vert & :(-4)\\t^2+\dfrac{1}{2}t-1 &=& 0 &\vert &\text{p-q-Formel}\\t_{1,2} &=& -\dfrac{1}{4}\pm\sqrt{\left(\dfrac{1}{4}\right)^2+1}\\t_{1,2} &=& -\dfrac{1}{4}\pm\sqrt{\dfrac{17}{16}}\\\\t_1 &=& \dfrac{-1+\sqrt{17}}{4} \approx 0{,}78 \;\in\;\mathbb{D}\\t_2 &=& \dfrac{-1-\sqrt{17}}{4} \approx -1{,}28 \;\not\in\;\mathbb{D}\end{array}