Question

\(\left(\left|x\right|-\dfrac{3}{2}\right)^2=\dfrac{14}{25}-\dfrac{1}{5}\)

Answer 1

\(\left(\left|x\right|-\dfrac{3}{2}\right)^2=\dfrac{9}{25}\Rightarrow\left[{}\begin{matrix}\left|x\right|-\dfrac{3}{2}=\dfrac{3}{5}\\\left|x\right|-\dfrac{3}{2}=-\dfrac{3}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left|x\right|=\dfrac{21}{10}\\\left|x\right|=\dfrac{9}{10}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{21}{10}\\x=-\dfrac{21}{10}\\x=\dfrac{9}{10}\\x=-\dfrac{9}{10}\end{matrix}\right.\)