Question

Resolva a equação (n+1)!/(n-1)!=2, e encontre o valor de n: ​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{\dfrac{(n + 1)!}{(n - 1)!} = 2}$

$\mathsf{\dfrac{n.(n + 1).(n - 1)!}{(n - 1)!} = 2}$

$\mathsf{n(n + 1) = 2}$

$\mathsf{n^2 + n = 2}$

$\mathsf{n^2 + n - 2 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = 1^2 - 4.1.(-2)}$

$\mathsf{\Delta = 1 + 8}$

$\mathsf{\Delta = 9}$

$\mathsf{n = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-1 \pm \sqrt{9}}{2} \rightarrow \begin{cases}\mathsf{n' = \dfrac{-1 + 3}{2} = \dfrac{2}{2} = 1}\\\\\mathsf{n'' = \dfrac{-1 - 3}{2} = \dfrac{-4}{2} = -2}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{1\}}}}$