Đáp án:
6) 2
Giải thích các bước giải:
\(\begin{array}{l}
3)\dfrac{{\left( {9\sqrt 7 - 19} \right)\left( {3 + \sqrt 7 } \right)}}{{9 - 7}} + \dfrac{{\left( {\sqrt 7 + 1} \right)\left( {\sqrt 7 - 3} \right)}}{{7 - 9}} - \dfrac{{\left( {33 - 9\sqrt 7 } \right)\left( {\sqrt 7 + 2} \right)}}{{7 - 4}}\\
= \dfrac{{27\sqrt 7 + 63 - 57 - 19\sqrt 7 }}{2} + \dfrac{{7 - 3\sqrt 7 + \sqrt 7 - 3}}{{ - 2}} - \dfrac{{33\sqrt 7 + 66 - 63 - 18\sqrt 7 }}{3}\\
= \dfrac{{8\sqrt 7 + 6}}{2} - \dfrac{{4 - 2\sqrt 7 }}{2} - \dfrac{{15\sqrt 7 + 3}}{3}\\
= 4\sqrt 7 + 3 - 2 + \sqrt 7 - 5\sqrt 7 - 1 = 0\\
4)\dfrac{{\left( {5 + \sqrt 5 } \right)\left( {\sqrt 5 - 2} \right)}}{{5 - 4}} + \dfrac{{\sqrt 5 \left( {\sqrt 5 + 1} \right)}}{{5 - 1}} - \dfrac{{3\sqrt 5 \left( {3 - \sqrt 5 } \right)}}{{9 - 5}}\\
= \dfrac{{5\sqrt 5 - 10 + 5 - 2\sqrt 5 }}{1} + \dfrac{{5 + \sqrt 5 }}{4} - \dfrac{{9\sqrt 5 - 15}}{4}\\
= \dfrac{{4\left( {3\sqrt 5 - 5} \right) + 5 + \sqrt 5 - 9\sqrt 5 + 15}}{4}\\
= \dfrac{{12\sqrt 5 - 20 + 5 + \sqrt 5 - 9\sqrt 5 + 15}}{4}\\
= \dfrac{{4\sqrt 5 }}{4} = \sqrt 5 \\
6)\dfrac{1}{{\sqrt {2 - 2\sqrt 2 .1 + 1} }} - \dfrac{1}{{\sqrt {2 + 2\sqrt 2 .1 + 1} }}\\
= \dfrac{1}{{\sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}} }} - \dfrac{1}{{\sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} }}\\
= \dfrac{1}{{\sqrt 2 - 1}} - \dfrac{1}{{\sqrt 2 + 1}}\\
= \dfrac{{\sqrt 2 + 1 - \sqrt 2 + 1}}{{2 - 1}} = 2
\end{array}\)
