Question

Find the 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 $\left|\begin{array}{cc}3& x\\ x& 1\end{array}\right|=\left|\begin{array}{cc}3& 2\\ 4& 1\end{array}\right|$

Solving the determinants, we get:

$3-x^2=3-8$

$x^2=8$

$x=\pm 2\sqrt{2}$