Đáp án:
\(\begin{array}{l}
4)D = 2\\
5)E = - 2 - 4\sqrt 3 \\
6)F = 2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
4)D = \dfrac{{\sqrt 5 \left( {\sqrt {\sqrt 5 + 1} + 1} \right)}}{{\sqrt 5 + 1 - 1}} - \dfrac{{\sqrt 5 \left( {\sqrt {\sqrt 5 + 1} - 1} \right)}}{{\sqrt 5 + 1 - 1}}\\
= \sqrt {\sqrt 5 + 1} + 1 - \left( {\sqrt {\sqrt 5 + 1} - 1} \right)\\
= 2\\
5)E = \dfrac{{2\left( {\sqrt 2 + 1} \right)}}{{2 - 1}} - \dfrac{{2\left( {\sqrt 3 + \sqrt 2 } \right)}}{{3 - 2}} - \dfrac{{2\left( {\sqrt 4 + \sqrt 3 } \right)}}{{4 - 3}}\\
= 2\left( {\sqrt 2 + 1} \right) - 2\left( {\sqrt 3 + \sqrt 2 } \right) - 2\left( {\sqrt 4 + \sqrt 3 } \right)\\
= 2\sqrt 2 + 2 - 2\sqrt 3 - 2\sqrt 2 - 4 - 2\sqrt 3 \\
= - 2 - 4\sqrt 3 \\
6)F = \dfrac{{1 + \sqrt 2 }}{{1 - 2}} - \dfrac{{\sqrt 2 + \sqrt 3 }}{{2 - 3}} + \dfrac{{\sqrt 3 + \sqrt 4 }}{{3 - 4}} - \dfrac{{\sqrt 4 + \sqrt 5 }}{{4 - 5}} + \dfrac{{\sqrt 5 + \sqrt 6 }}{{5 - 6}} - \dfrac{{\sqrt 6 + \sqrt 7 }}{{6 - 7}} + \dfrac{{\sqrt 7 + \sqrt 8 }}{{7 - 8}} - \dfrac{{\sqrt 8 + \sqrt 9 }}{{8 - 9}}\\
= - 1 - \sqrt 2 + \sqrt 2 + \sqrt 3 - \sqrt 3 - \sqrt 4 + \sqrt 4 + \sqrt 5 - \sqrt 5 - \sqrt 6 + \sqrt 6 + \sqrt 7 - \sqrt 7 - \sqrt 8 + \sqrt 8 + \sqrt 9 \\
= - 1 + \sqrt 9 = - 1 + 3 = 2
\end{array}\)
