a) \(\sqrt{x}-1=\dfrac{1}{2}\left(đk:x\ge0\right)\)
\(\Rightarrow\sqrt{x}=\dfrac{3}{2}\Rightarrow x=\dfrac{9}{4}\)(nhận)
b) \(\sqrt{\left(5x+1\right)^2}=\dfrac{6}{7}\)
\(\Rightarrow\left|5x+1\right|=\dfrac{6}{7}\)
\(\Rightarrow\left[{}\begin{matrix}5x+1=\dfrac{6}{7}\\5x+1=-\dfrac{6}{7}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{35}\\x=-\dfrac{13}{35}\end{matrix}\right.\)
c) \(\dfrac{3}{4}-\left|x-\dfrac{3}{2}\right|=\dfrac{1}{6}\)
\(\Rightarrow\left|x-\dfrac{3}{2}\right|=\dfrac{7}{12}\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{3}{2}=\dfrac{7}{12}\\x-\dfrac{3}{2}=-\dfrac{7}{12}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{25}{12}\\x=\dfrac{11}{12}\end{matrix}\right.\)
d) \(\left(\left|x-1\right|-2\right)\left(-\dfrac{1}{2}x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\left|x-1\right|-2=0\\-\dfrac{1}{2}x-2=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left|x-1\right|=2\\x=-4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-1=2\\x-1=-2\\x=-4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=3\\x=-1\\x=-4\end{matrix}\right.\)
f) \(\left(\left|x\right|-1\right)\left(x^2+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\left|x\right|-1=0\\x^2+2=0\left(VLý\right)\end{matrix}\right.\)
\(\Rightarrow\left|x\right|=1\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
