Đáp án:
a, \[A = 3 - 3\sqrt 5 \]
b,
\[B = 2 + \sqrt 3 \]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = \frac{4}{{\sqrt 5 + 3}} - \sqrt {20} = \frac{{4\left( {\sqrt 5 - 3} \right)}}{{\left( {\sqrt 5 - 3} \right)\left( {\sqrt 5 + 3} \right)}} - \sqrt {{2^2}.5} \\
= \frac{{4\left( {\sqrt 5 - 3} \right)}}{{5 - 5}} - 2\sqrt 5 = - \left( {\sqrt 5 - 3} \right) - 2\sqrt 5 = 3 - 3\sqrt 5
\end{array}\)
\(\begin{array}{l}
B = \frac{{1 + \sqrt 3 }}{{\sqrt {4 - 2\sqrt 3 } }} = \frac{{1 + \sqrt 3 }}{{\sqrt {3 - 2\sqrt 3 + 1} }} = \frac{{1 + \sqrt 3 }}{{\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} }}\\
= \frac{{\sqrt 3 + 1}}{{\sqrt 3 - 1}} = \frac{{{{\left( {\sqrt 3 + 1} \right)}^2}}}{{\left( {\sqrt 3 - 1} \right)\left( {\sqrt 3 + 1} \right)}} = \frac{{4 + 2\sqrt 3 }}{2} = 2 + \sqrt 3
\end{array}\)
