Question

Find a value of $x$ if $\left|\begin{array}{cc}x& 2\\ 18& x\end{array}\right|=\left|\begin{array}{cc}6& 2\\ 18& 6\end{array}\right|$

Answer 1

$\left|\begin{array}{cc}x& 2\\ 18& x\end{array}\right|=\left|\begin{array}{cc}6& 2\\ 18& 6\end{array}\right|$

$x^2-18\times 2=6\times 6-2\times 18$

$x^2-36=36-36$

$x=\pm 6$