Quadratwurzel/Linearkombination/Rechnung/2/Aufgabe/Lösung

Es ist

${}{\begin{aligned}{\left({\frac {2}{5}}-{\frac {3}{7}}{\sqrt {3}}\right)}\cdot {\left({\frac {1}{4}}-{\frac {2}{3}}{\sqrt {3}}\right)}&={\frac {1}{10}}-{\frac {4}{15}}{\sqrt {3}}-{\frac {3}{28}}{\sqrt {3}}+{\frac {2}{7}}\cdot {\sqrt {3}}^{2}\\&={\frac {1}{10}}+{\frac {6}{7}}-{\left({\frac {4}{15}}+{\frac {3}{28}}\right)}{\sqrt {3}}\\&={\frac {7+60}{70}}-{\frac {112+45}{420}}{\sqrt {3}}\\&={\frac {67}{70}}-{\frac {157}{420}}{\sqrt {3}}.\end{aligned}}$

Zur gelösten Aufgabe