Question

Me ajudemmm por favor

Answer 1

$\text{Sabemos\ que}\begin{vmatrix}a & b\\c & d\end{vmatrix} =ad-bc \\ \\ \text{Portanto} \\ \\ \begin{vmatrix}x & 3\\x+1 & x-1\end{vmatrix} =2\Longrightarrow x( x-1) -3( x+1) =2\Longrightarrow \\ \\ \Longrightarrow x^{2} -4x-5=0 \\ \\ \Delta =b^{2} -4ac=( -4)^{2} -4\cdotp 1\cdotp ( -5) =36 \\ \\ x=\frac{-b\pm \sqrt{\Delta }}{2a} =\frac{4\pm 6}{2\cdotp 1} \Longrightarrow x=-1\lor x=5 \\ \\ \therefore \boxed{\boxed{S=\{x\in \mathbb{R} |x=-1\lor x=5\}}}$