Tìm x của biểu thức, biết: a) 1/5 − x = − 3/4 ; b) ( x − 215 )^3 = 8 /125 ;

10/14

(1,75 điểm) Tìm x, biết:

a) \(\frac{1}{5} - x = \frac{{ - 3}}{4}\);

b) \({\left( {x - \frac{2}{{15}}} \right)^3} = \frac{8}{{125}}\);

c) \(\left| {\frac{8}{3} - 3x} \right| - \frac{2}{3} = \frac{1}{2}\).

Nhập câu trả lời ở đây

0/3000 ký tự

Giải thích

a) \(\frac{1}{5} - x = \frac{{ - 3}}{4}\)

\(x = \frac{1}{5} + \frac{3}{4}\)

\(x = \frac{{19}}{{20}}\)

Vậy \(x = \frac{{19}}{{20}}\).

b) \({\left( {x - \frac{2}{{15}}} \right)^3} = \frac{8}{{125}}\)

\({\left( {x - \frac{2}{{15}}} \right)^3} = {\left( {\frac{2}{5}} \right)^3}\)

Suy ra \(x - \frac{2}{{15}} = \frac{2}{5}\)

\(x = \frac{2}{5} + \frac{2}{{15}}\)

\(x = \frac{8}{{15}}\)

Vậy \(x = \frac{8}{{15}}\).

c) \(\left| {\frac{8}{3} - 3x} \right| - \frac{2}{3} = \frac{1}{2}\)

\(\left| {\frac{8}{3} - 3x} \right| = \frac{1}{2} + \frac{2}{3}\)

\(\left| {\frac{8}{3} - 3x} \right| = \frac{7}{6}\)

Trường hợp 1:

\(\frac{8}{3} - 3x = \frac{7}{6}\)

\(3x = \frac{8}{3} - \frac{7}{6}\)

\(3x = \frac{9}{6} = \frac{3}{2}\)

\(x = \frac{3}{2}:3\)

\(x = \frac{1}{2}\)

Vậy \(x \in \left\{ {\frac{1}{2};\frac{{23}}{{18}}} \right\}\).

Trường hợp 2:

\(\frac{8}{3} - 3x = - \frac{7}{6}\)

\(3x = \frac{8}{3} + \frac{7}{6}\)

\(3x = \frac{{23}}{6}\)

\(x = \frac{{23}}{6}:3\)

\(x = \frac{{23}}{{18}}\)