Hãy thu gọn ​\(\begin{aligned} & \sqrt {\frac{1}{9}{{\left( {x + \frac{1}{2}} \right)}^2}} \left( {x...

Câu hỏi :

Thu gọn \(\begin{aligned} & \sqrt {\frac{1}{9}{{\left( {x + \frac{1}{2}} \right)}^2}} \left( {x < - \frac{1}{2}} \right) \end{aligned} \) ta được:

A.  \( - \frac{1}{3}\left( {x + \frac{1}{2}} \right)\)

B.  \(\frac{1}{3}\left( {x + \frac{1}{2}} \right)\)

C.  \( \frac{1}{9}\left( {x + \frac{1}{2}} \right)\)

D.  \( - \frac{1}{6}\left( {x + \frac{1}{2}} \right)\)

* Đáp án

A

* Hướng dẫn giải

 \(\begin{aligned} & \sqrt {\frac{1}{9}{{\left( {x + \frac{1}{2}} \right)}^2}} \\ & = \sqrt {\frac{1}{9}} .\sqrt {x + \frac{1}{2}} \\ & = \frac{1}{3}.\left| {x + \frac{1}{2}} \right|\\ & = - \frac{1}{3}\left( {x + \frac{1}{2}} \right)\left( { \text{ Do } x < - \frac{1}{2} \Rightarrow x + \frac{1}{2} < 0} \right) \end{aligned} \)

Copyright © 2021 HOCTAP247