Question

Resolva a equação.


$\frac{(n+1)!}{(n-1)!}=12$

Answer 1

Olá, Felipe.

$\frac{(n+1)!}{(n-1)!}=12\Rightarrow\\\\ \frac{(n+1)n(n-1)!}{(n-1)!}=12\Rightarrow\\\\ (n+1)n=12\Rightarrow\\\\ n^2+n=12\Rightarrow\\\\ n^2+n-12=0\Rightarrow\\\\ n=\frac{-1\pm\sqrt{1+48}}{2}=\frac{-1\pm\sqrt{49}}{2}=\frac{-1\pm7}{2}\Rightarrow\\\\ n=-4\text{ (imposs\'ivel)}\text{ ou }\boxed{n=3}$