Question

If $\left|\begin{array}{cc}2x& 5\\ 8& x\end{array}\right|=\left|\begin{array}{cc}6& -2\\ 7& 3\end{array}\right|$, write the value of x.

Answer 1

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