Question

Find values of $x$ for which $\left|\begin{array}{cc}3& x\\ x& 1\end{array}\right|=\left|\begin{array}{cc}3& 2\\ 4& 1\end{array}\right|$

Answer 1

Given: $\left|\begin{array}{cc}3& x\\ x& 1\end{array}\right|=\left|\begin{array}{cc}3& 2\\ 4& 1\end{array}\right|$
$\Rightarrow 3\left(1\right)-x\left(x\right)=3\left(1\right)-4\left(2\right)$
$\Rightarrow 3-x^2=3-8$
$\Rightarrow 3-x^2=-5$
$\Rightarrow -x^2=-5-3$
$\Rightarrow -x^2=-8$
$\Rightarrow x^2=8$
$\Rightarrow x=\pm \sqrt{8}=\pm 2\sqrt{2}$
Hence value of $x$ is $\pm 2\sqrt{2}$