Đáp án:
$1.$
$a. \frac{3}{5}$
$b. \frac{32}{5}$
$2.$
$a. x = \frac{36}{25}$
$b.$ \(\left[ \begin{array}{l}x= - \frac{13}{15}\\x=\frac{17}{15}\end{array} \right.\)
Giải thích các bước giải:
$1. a. \sqrt[]{\frac{1}{9}} . \sqrt[]{0,81} + \sqrt[]{0,09}$
$= \frac{1}{3} . \sqrt[]{\frac{81}{100}} + \sqrt[]{\frac{9}{100}}$
$= \frac{1}{3} . \frac{9}{10} + \frac{3}{10}$
$= \frac{3}{10} + \frac{3}{10}$
$= \frac{6}{10}$
$= \frac{3}{5}$
$2. ( \frac{2}{5}\sqrt[]{16} + 2\sqrt[]{\frac{16}{25}} ) : 2\sqrt[]{\frac{1}{16}}$
$= ( \frac{2}{5} . 4 + 2 . \frac{4}{5} ) : ( 2 . \frac{1}{4} )$
$= ( \frac{8}{5} + \frac{8}{5} ) : \frac{1}{2}$
$= \frac{16}{5} . 2$
$= \frac{32}{5}$
$2. a. \frac{5}{12}\sqrt[]{x} - \frac{1}{6} = \frac{1}{3}$ $( x ≥ 0 )$
$⇔ \frac{5}{12}\sqrt[]{x} - \frac{2}{12} = \frac{4}{12}$
$⇔ 5\sqrt[]{x} - 2 = 4$
$⇔ 5\sqrt[]{x} = 6$
$⇔ \sqrt[]{x} = \frac{6}{5}$
$⇔ x = \frac{36}{25}$
$b. ( \frac{1}{5} - \frac{3}{2}x )^{2} = \frac{9}{4}$
TH1 : $\frac{1}{5} - \frac{3}{2}x = \frac{3}{2}$
$⇔ \frac{2}{10} - \frac{15}{10}x = \frac{15}{10}$
$⇔ 2 - 15x = 15$
$⇔ 15x = 2 - 15$
$15x = - 13$
$⇔ x = - \frac{13}{15}$
TH2 : $\frac{1}{5} - \frac{3}{2}x = - \frac{3}{2}$
$⇔ \frac{2}{10} - \frac{15}{10}x = - \frac{15}{10}$
$⇔ 2 - 15x = - 15$
$⇔ 15x = 2 + 15$
$⇔ 15x = 17$
$⇔ x = \frac{17}{15}$
Kết hợp 2TH ⇒ \(\left[ \begin{array}{l}x= - \frac{13}{15}\\x=\frac{17}{15}\end{array} \right.\)
