a) \(\left|x.\left(x^2-\frac{5}{4}\right)\right|=x\)
\(\Rightarrow\left[{}\begin{matrix}x.\left(x^2-\frac{5}{4}\right)=x\\x.\left(x^2-\frac{5}{4}\right)=-x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x^3-\frac{5}{4}x=x\\x^3-\frac{5}{4}x=-x\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^3-\frac{5}{4}x-x=0\\x^3-\frac{5}{4}x+x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x^3-\left(\frac{5}{4}x+x\right)=0\\x^3-\left(\frac{5}{4}x-x\right)=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^3-\frac{9}{4}x=0\\x^3-\frac{1}{4}x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x.\left(x^2-\frac{9}{4}\right)=0\\x.\left(x^2-\frac{1}{4}\right)=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\\x^2-\frac{9}{4}=0\end{matrix}\right.\\\left[{}\begin{matrix}x=0\\x^2-\frac{1}{4}=0\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\\x^2=\frac{9}{4}\end{matrix}\right.\\\left[{}\begin{matrix}x=0\\x^2=\frac{1}{4}\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=\frac{3}{2}\\x=-\frac{3}{2}\end{matrix}\right.\end{matrix}\right.\\\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=\frac{1}{2}\\x=-\frac{1}{2}\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\)
Vậy \(x\in\left\{0;\frac{3}{2};-\frac{3}{2};\frac{1}{2};-\frac{1}{2}\right\}.\)
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