Question:
If $\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 7 & 3\end{array}\right|$, then $x=$
(a) 3
(b) $\pm 3$
(c) $\pm 6$
(d) 6
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 correct option is (c).
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