Toán Lớp 9: |căn x / (x – căn x +1)| = 2/3
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 9: |căn x / (x – căn x +1)| = 2/3
Comments ( 1 )
Giải đáp: $x = \dfrac{1}{4};x = 4$
Lời giải và giải thích chi tiết:
$\begin{array}{l}
Dkxd:x \ge 0\\
\left| {\dfrac{{\sqrt x }}{{x – \sqrt x + 1}}} \right| = \dfrac{2}{3}\\
\Leftrightarrow \dfrac{{\sqrt x }}{{x – \sqrt x + 1}} = \dfrac{2}{3}\left( {do:\left\{ \begin{array}{l}
\sqrt x \ge 0\\
x + \sqrt x + 1 > 0
\end{array} \right.} \right)\\
\Leftrightarrow 3\sqrt x = 2x – 2\sqrt x + 2\\
\Leftrightarrow 2x – 5\sqrt x + 2 = 0\\
\Leftrightarrow \left( {2\sqrt x – 1} \right)\left( {\sqrt x – 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt x = \dfrac{1}{2}\\
\sqrt x = 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{1}{4}\\
x = 4
\end{array} \right.\left( {tm} \right)\\
Vậy\,x = \dfrac{1}{4};x = 4
\end{array}$