TeX Quellcode:

\begin{array}{crclcl} & \mathbb{D} &=& \mathbb{R} \cr\cr & 0 &=& x^4+5x^3-x^3\ln(5)-x^25\ln(5) \cr & 0 &=& x^2\left[x^2+\left(5-\ln(5)\right)x-5\ln(5)\right] &\vert& \text{Satz vom Nullprodukt} \cr \text{Faktor 1:} & x^2 &=& 0 &\vert& \pm\sqrt{} \cr& x_1 &=& 0 \cr\cr\text{Faktor 2:} & x^2+\left(5-\ln(5)\right)x-5\ln(5) &=& 0 &\vert& \text{p-q-Formel} \cr & x_{2,3} &=& -\dfrac{5-\ln(5)}{2}\pm\sqrt{\left(\dfrac{5-\ln(5)}{2}\right)^2+5\ln(5)} \cr & x_{2,3} &=& -\dfrac{5-\ln(5)}{2}\pm\sqrt{\dfrac{25-10\ln(5)+\left(\ln(5)\right)^2}{4}+\dfrac{20\ln(5)}{4}} \cr\cr & x_{2,3} &=& -\dfrac{5-\ln(5)}{2}\pm\sqrt{\dfrac{25+10\ln(5)+\left(\ln(5)\right)^2}{4}} \cr\cr & x_{2,3} &=& -\dfrac{5-\ln(5)}{2}\pm\sqrt{\left(\dfrac{5+\ln(5)}{2}\right)^2} \cr\cr & x_{2,3} &=& -\dfrac{5-\ln(5)}{2}\pm\dfrac{5+\ln(5)}{2} \cr\cr & x_2 &=& -\dfrac{5-\ln(5)}{2}+\dfrac{5+\ln(5)}{2} = \dfrac{-\left(5-\ln(5)\right)+\left(5+\ln(5)\right)}{2} = \dfrac{2\ln(5)}{2} = \ln(5) \cr\cr & x_3 &=& -\dfrac{5-\ln(5)}{2}-\dfrac{5+\ln(5)}{2} = \dfrac{-\left(5-\ln(5)\right)-\left(5+\ln(5)\right)}{2} = -5 \cr\cr & \mathbb{L} &=& \{-5; 0; \ln(5)\} \end{array}