Đáp án:
\(\begin{array}{l}
13) - 4\sqrt 3 \\
14)6\\
15)6
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
13)\dfrac{{\left( {\sqrt 2 + \sqrt 3 } \right)\left( {2 + \sqrt 6 } \right) + \left( {\sqrt 3 - \sqrt 2 } \right)\left( {2 - \sqrt 6 } \right)}}{{4 - 6}}\\
= \dfrac{{2\sqrt 2 + 2\sqrt 3 + 2\sqrt 3 + 3\sqrt 2 + 2\sqrt 3 - 3\sqrt 2 - 2\sqrt 2 + 2\sqrt 3 }}{{ - 2}}\\
= \dfrac{{8\sqrt 3 }}{{ - 2}} = - 4\sqrt 3 \\
14)\dfrac{{\sqrt 5 \left( {2 - 7\sqrt 3 } \right)}}{{2 - 7\sqrt 3 }} + \dfrac{{31\left( {6 - \sqrt 5 } \right)}}{{36 - 5}}\\
= \sqrt 5 + 6 - \sqrt 5 = 6\\
15)\dfrac{{3\left( {\sqrt 2 - \sqrt 3 } \right)}}{{\sqrt 2 - \sqrt 3 }} + \sqrt 3 + \dfrac{{6\left( {3 - \sqrt 3 } \right)}}{{9 - 3}}\\
= 3 + \sqrt 3 + 3 - \sqrt 3 = 6
\end{array}\)
