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Question
Find the value of x, if
\[\begin{vmatrix}3 & x \\ x & 1\end{vmatrix} = \begin{vmatrix}3 & 2 \\ 4 & 1\end{vmatrix}\]
Solution
\[\text{ Given }: \begin{vmatrix}3 & x \\ x & 1\end{vmatrix} = \begin{vmatrix}3 & 2 \\ 4 & 1\end{vmatrix}\]
\[ \Rightarrow 3 - x^2 = 3 - 8\]
\[ \Rightarrow - x^2 = - 8\]
\[ \Rightarrow x^2 = 8\]
\[ \Rightarrow x = \pm 2\sqrt{2}\]
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