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Question:

If $x \in \mathrm{N}$ and $\left|\begin{array}{cc}x+3 & -2 \\ -3 x & 2 x\end{array}\right|=8$, then find the value of $x$.

Solution:

$\left|\begin{array}{cc}x+3 & -2 \\ -3 x & 2 x\end{array}\right|=8$

$\Rightarrow(x+3) 2 x-(-2)(-3 x)=8$

$\Rightarrow 2 x^{2}+6 x-6 x=8$

$\Rightarrow 2 x^{2}=8$

$\Rightarrow x^{2}-4=0$

$\Rightarrow x^{2}=4$

$\Rightarrow x=2 \quad[x \neq-2 \because x \in \mathrm{N}]$

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