Question

If $\left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right|$, then write the value of x.

Answer 1

$$\begin{gathered} \left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right| \\ \Rightarrow \left(x+1\right)\left(x+2\right)-\left(x-1\right)\left(x-3\right)=12+1 \\ \Rightarrow x^2+3x+2-x^2+4x-3=13 \\ \Rightarrow 7x-1=13 \\ \Rightarrow 7x=14 \\ \Rightarrow x=2 \\ \mathrm{Hence},\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{is}2. \end{gathered}$$