TeX Quellcode:

\begin{array}{rclll} 2+\sqrt[3]{x^3-4x^2+8x-14} &=& x &\vert & -2\\\sqrt[3]{x^3-4x^2+8x-14} &=& x-2 &\vert & ()^3\\x^3-4x^2+8x-14 &=& (x-2)(x-2)(x-2) \\x^3-4x^2+8x-14 &=& (x^2-4x+4)(x-2) \\x^3-4x^2+8x-14 &=& x^3-2x^2-4x^2+8x+4x-8 \\x^3-4x^2+8x-14 &=& x^3-6x^2+12x-8 &\vert & -x^3+6x^2-12x+8\\2x^2-4x-6 &=& 0 &\vert & :2\\x^2-2x-3 &=& 0 &\vert & \text{p-q-Formel}\\x_{1,2} &=& 1\pm\sqrt{1+3}\\x_{1,2} &=& 1\pm\sqrt{4}\\\\x_1 &=& 1+2 = 3 \;\in\;\mathbb{D}\\x_2 &=& 1-2 = -1\;\in\;\mathbb{D}\end{array}