TeX Quellcode:

\begin{array}{lrclcl}& 0 &=& \dfrac{x}{\sqrt{3}}+\sqrt[3]{3x^2}\cdot \sqrt[3]{3^2} &\vert& -\dfrac{x}{\sqrt{3}} \\\\ & -\dfrac{x}{\sqrt{3}} &=& \sqrt[3]{3x^2\cdot3^2} \\\\ & -\dfrac{x}{\sqrt{3}} &=& \sqrt[3]{27x^2} &\vert& ()^3 \\\\ & -\dfrac{x^3}{\left(\sqrt{3}\right)^3} &=& 27x^2 &\vert& +\dfrac{x^3}{\left(\sqrt{3}\right)^3} \\\\ & 0 &=& 27x^2+\dfrac{x^3}{\left(\sqrt{3}\right)^3} \\\\ & 0 &=& x^2\cdot\left(27+\dfrac{x}{\left(\sqrt{3}\right)^3}\right) &\vert& \text{Satz vom Nullprodukt} \\\\ \text{Faktor 1:} & x^2 &=& 0 &\vert& \pm\sqrt{} \\\\ & x_1 &=& 0 \in \mathbb{D} \\\\\\\text{Faktor 2:} & 0 &=& 27+\dfrac{x}{\left(\sqrt{3}\right)^3} &\vert& -\dfrac{x}{\left(\sqrt{3}\right)^3} \\\\ & -\dfrac{x}{\left(\sqrt{3}\right)^3} &=& 3^3 &\vert& \cdot \left(-\left(\sqrt{3}\right)^3\right) \\\\ & x &=& 3^3\cdot\left(-\left(\sqrt{3}\right)^3\right) \\& x &=& -(\sqrt{3})^{2 \cdot 3}\cdot (\sqrt{3})^3 \\& x &=& -(\sqrt{3})^9 \\\\ & x_2 &=& -\sqrt{3^9} \approx -140{,}30 \in \mathbb{D}\end{array}