Question

If $\left|\begin{array}{cc}x& 2\\ 18& x\end{array}\right|=\left|\begin{array}{cc}6& 2\\ 3x& 6\end{array}\right|$, then $x$ is equal to

• A. $6$
• B. $\pm 6$
• C. $-6$
• D. $0$

Answer 1

Answer: (A)

$6$

$\left|\begin{array}{cc}x& 2\\ 18& x\end{array}\right|=\left|\begin{array}{cc}6& 2\\ 3x& 6\end{array}\right|$
$\Rightarrow x^2-36=36-6x$
$\Rightarrow x^2+6x-72=0$
$\Rightarrow x=\frac{-6\pm \sqrt{6^2+4\times 72}}{2}$
$=\frac{-6\pm \sqrt{36(1+8)}}{2}$
$=-3\pm 9=6or-12$