Question

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

Answer 1

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

$$\begin{gathered} \Rightarrow \left(x+3\right)2x-\left(-2\right)\left(-3x\right)=8 \\ \Rightarrow 2x^2+6x-6x=8 \\ \Rightarrow 2x^2=8 \\ \Rightarrow x^2-4=0 \\ \Rightarrow x^2=4 \\ \Rightarrow x=2\left[x\ne -2\because x\in \mathrm{N}\right] \end{gathered}$$