Tìm x: \({\left( {\frac{1}{5} – x} \right)^2} = \frac{{16}}{9}\)

Tìm x: \({\left( {\frac{1}{5} – x} \right)^2} = \frac{{16}}{9}\)

A. \(\left[ \begin{array}{l}x = – \frac{{17}}{{15}}\\x = \frac{{23}}{{15}}\end{array} \right.\)

B. \(\left[ \begin{array}{l}x = \frac{{17}}{{15}}\\x = – \frac{{23}}{{15}}\end{array} \right.\)

C. \(\left[ \begin{array}{l}x = \frac{{17}}{{15}}\\x = \frac{{23}}{{15}}\end{array} \right.\)

D. \(\left[ \begin{array}{l}x = – \frac{{17}}{{15}}\\x = – \frac{{23}}{{15}}\end{array} \right.\)

Hướng dẫn

Chọn đáp án là: A

Phương pháp giải:

Dựa vào lý thuyết lũy thừa để giải.

\({\left( {\frac{1}{5} – x} \right)^2} = \frac{{16}}{9} \Leftrightarrow \left| {\frac{1}{5} – x} \right| = \frac{4}{3}\)

\( \Leftrightarrow \left[ \begin{array}{l}\frac{1}{5} – x = \frac{4}{3}\\\frac{1}{5} – x = – \frac{4}{3}\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{1}{5} – \frac{4}{3}\\x = \frac{1}{5} + \frac{4}{3}\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = – \frac{{17}}{{15}}\\x = \frac{{23}}{{15}}\end{array} \right..\)

Chọn A.