Find values of $x$ for which $\begin{vmatrix} 3 & x \\ x & 1 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix}$.

$\pm 2\sqrt{2}$

The correct answer is Option (2) → $\pm 2\sqrt{2}$ ##

We have $\begin{vmatrix} 3 & x \\ x & 1 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix}$

i.e., $3 - x^2 = 3 - 8$

i.e., $x^2 = 8$

Hence $x = \pm 2\sqrt{2}$