Question

Solve:

$\left|\begin{array}{ccc}0& -3& x\\ x+1& 3& 1\\ 4& 1& 5\end{array}\right|$ =$0$

Answer 1

$\left|\begin{array}{ccc}0& -3& x\\ x+1& 3& 1\\ 4& 1& 5\end{array}\right|$ =$0$
$\begin{array}{c}0(3\times 5-1)+3(5\times (x+1)-4)+x(x+1-12)=0\\ 0+3\left[5x+5-4\right]+x\left[x-11\right]=0\\ 15x+3+x^2-11x=0\\ x^2+4x+3=0\\ x^2+3x+x+3=0\\ x(x+3)+1(x+3)=0\\ (x+1)(x+3)=0\\ \therefore x=-1,-3\end{array}$