Inequality question .

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ {\left|\mathrm{x}\right|}^2-\left|\mathrm{x}\right|+4=2{\mathrm{x}}^2-3\left|\mathrm{x}\right|+1 \\ \mathrm{As} {\mathrm{x}}^2={\left|\mathrm{x}\right|}^2, \mathrm{hence} \\ {\left|\mathrm{x}\right|}^2-\left|\mathrm{x}\right|+4=2{\left|\mathrm{x}\right|}^2-3\left|\mathrm{x}\right|+1 \\ \Rightarrow {\left|\mathrm{x}\right|}^2-2\left|\mathrm{x}\right|-3=0 \\ \Rightarrow {\left|\mathrm{x}\right|}^2-3\left|\mathrm{x}\right|+\left|\mathrm{x}\right|-3=0 \\ \Rightarrow \left|\mathrm{x}\right|\left(\left|\mathrm{x}\right|-3\right)+1\left(\left|\mathrm{x}\right|-3\right)=0 \\ \Rightarrow \left(\left|\mathrm{x}\right|-3\right)\left(\left|\mathrm{x}\right|+1\right)=0 \\ \Rightarrow \left|\mathrm{x}\right|=3 \mathrm{or} \left|\mathrm{x}\right|=-1 \\ \mathrm{But} \left|\mathrm{x}\right|=-1 \mathrm{is} \mathrm{not} \mathrm{possible}, \mathrm{hence} \\ \left|\mathrm{x}\right|=3 \\ \Rightarrow \mathrm{x}=\pm 3 \end{gathered}$$

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