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Question
If \[\begin{vmatrix}2x & 5 \\ 8 & x\end{vmatrix} = \begin{vmatrix}6 & - 2 \\ 7 & 3\end{vmatrix}\] , write the value of x.
Solution
\[\begin{vmatrix}2x & 5 \\ 8 & x\end{vmatrix} = \begin{vmatrix}6 & - 2 \\ 7 & 3\end{vmatrix}\]
\[ \Rightarrow 2 x^2 - 40 = 18 + 14\]
\[ \Rightarrow 2 x^2 - 40 = 32\]
\[ \Rightarrow 2 x^2 = 72\]
\[ \Rightarrow x^2 = 36\]
\[ \Rightarrow x = \pm 6\]
Hence, the value of x is \pm 6 .
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