Question

If x ∈ N and \[\begin{vmatrix}x + 3 & - 2 \\ - 3x & 2x\end{vmatrix}\]  = 8, then find the value of x.

Answer 1

\[\begin{vmatrix}x + 3 & - 2 \\ - 3x & 2x\end{vmatrix}\]  = 8

\[\Rightarrow \left( x + 3 \right)2x - \left( - 2 \right)\left( - 3x \right) = 8\]
\[ \Rightarrow 2 x^2 + 6x - 6x = 8\]
\[ \Rightarrow 2 x^2 = 8\]
\[ \Rightarrow x^2 - 4 = 0\]
\[ \Rightarrow x^2 = 4\]
\[ \Rightarrow x = 2 \left[ x \neq - 2 \because x \in N \right]\]