\(x\left|x^2-\frac{5}{4}\right|=x\)
\(\left|x^2-\frac{5}{4}\right|=x\text{ : }x\)
\(\left|x^2-\frac{5}{4}\right|=1\)
\(\Rightarrow\orbr{\begin{cases}x^2-\frac{5}{4}=-1\\x^2-\frac{5}{4}=1\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x^2=-1+\frac{5}{4}\\x^2=1+\frac{5}{4}\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x^2=\frac{1}{4}\\x^2=\frac{9}{4}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x^2=\left(\pm\frac{1}{2}\right)^2\\x^2=\left(\pm\frac{3}{2}\right)^2\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=\pm\frac{1}{2}\\x=\pm\frac{3}{2}\end{cases}}\)
\(^{\text{*}}0\text{ }\) là một giá tị thỏa mãn đề bài
\(\Rightarrow\text{ }x\in\left\{-\frac{1}{2}\text{ ; }\frac{1}{2}\text{ ; }-\frac{3}{2}\text{ ; }\frac{3}{2}\text{ ; }0\right\}\)