Question

Determine a solução da equação(x + 2)!/x!= 6, com x >0.​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{\dfrac{(x + 2)!}{x!} = 6}$

$\mathsf{\dfrac{(x + 2).(x + 1).x!}{x!} = 6}$

$\mathsf{(x + 2).(x + 1) = 6}$

$\mathsf{x^2 + 3x + 2 = 6}$

$\mathsf{x^2 + 3x - 4 = 0}$

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

$\mathsf{\Delta = (3)^2 - 4.1.(-4)}$

$\mathsf{\Delta = 9 + 16}$

$\mathsf{\Delta = 25}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-3 \pm \sqrt{25}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{-3 + 5}{2} = \dfrac{2}{2} = 1}\\\\\mathsf{x'' = \dfrac{-3 - 5}{2} = \dfrac{-8}{2} = -4}\end{cases}}$

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