Question:
If $\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 7 & 3\end{array}\right|$, write the value of $x$
Solution:
$\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 7 & 3\end{array}\right|$
$\Rightarrow 2 x^{2}-40=18+14$
$\Rightarrow 2 x^{2}-40=32$
$\Rightarrow 2 x^{2}=72$
$\Rightarrow x^{2}=36$
$\Rightarrow x=\pm 6$
Hence, the value of $x$ is $\pm 6$.
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