Question

The value of $x,$ if
$\left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right|$ is

• A. $4$
• B. $-4$
• C. $2$
• D. $5$

Answer 1

The correct option is C $2$

$\left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right|$
$\Rightarrow (x+1)(x+2)-(x-1)(x-3)=4\times 3-1\times (-1)$
$\Rightarrow (x^2+2x+x+2)-(x^2-3x-x+3)=12+1$
$\Rightarrow 7x-1=13$
$\Rightarrow x=2$