Đáp án:
\(\begin{array}{l}
B1:\\
a)18\sqrt 3 + 8\sqrt 5 \\
b)10\\
c)11\\
B2:\\
a)x = 44\\
b)\left[ \begin{array}{l}
x = \dfrac{4}{5}\\
x = - \dfrac{2}{5}
\end{array} \right.
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
B1:\\
a)3.3\sqrt 3 - 10.\dfrac{{\sqrt 5 }}{5} + 9\sqrt 3 + 2.5\sqrt 5 \\
= 18\sqrt 3 + 8\sqrt 5 \\
b)\sqrt {25 + 2.5.3\sqrt 2 + 18} + \left| {3\sqrt 2 - 5} \right|\\
= \sqrt {{{\left( {5 + 3\sqrt 2 } \right)}^2}} + 5 - 3\sqrt 2 \\
= 5 + 3\sqrt 2 + 5 - 3\sqrt 2 = 10\\
c)\left( {2\sqrt 5 - 3} \right)\sqrt {20 + 2.2\sqrt 5 + 9} \\
= \left( {2\sqrt 5 - 3} \right)\sqrt {{{\left( {2\sqrt 5 + 3} \right)}^2}} \\
= \left( {2\sqrt 5 - 3} \right)\left( {2\sqrt 5 + 3} \right)\\
= 20 - 9 = 11\\
B2:\\
a)DK:x \ge - 5\\
4\sqrt {x + 5} + 8.\dfrac{{\sqrt {x + 5} }}{4} - \sqrt {9\left( {x + 5} \right)} = 21\\
\to 4\sqrt {x + 5} + 2\sqrt {x + 5} - 3\sqrt {x + 5} = 21\\
\to 3\sqrt {x + 5} = 21\\
\to \sqrt {x + 5} = 7\\
\to x + 5 = 49\\
\to x = 44\\
b)\sqrt {49{{\left( {5x - 1} \right)}^2}} = 21\\
\to 7\left| {5x - 1} \right| = 21\\
\to \left| {5x - 1} \right| = 3\\
\to \left[ \begin{array}{l}
5x - 1 = 3\\
5x - 1 = - 3
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{4}{5}\\
x = - \dfrac{2}{5}
\end{array} \right.
\end{array}\)
