Question

o conjunto de solução da equação (n - 2)! = 2(n - 4)! é:
a) {1}
b) {2}
c) {4}
d) {6}
e) {1,4}​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{(n - 2)! = 2(n - 4)!}$

$\mathsf{(n - 2).(n - 3).(n - 4)! = 2(n - 4)!}$

$\mathsf{(n - 2).(n - 3) = 2}$

$\mathsf{n^2 -3n - 2n + 6 = 2}$

$\mathsf{n^2 -5n + 4 = 0}$

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

$\mathsf{\Delta = (-5)^2 - 4.1.4}$

$\mathsf{\Delta = 25 - 16}$

$\mathsf{\Delta = 9}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{5 \pm \sqrt{9}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{5 + 3}{2} = \dfrac{8}{2} = 4}\\\\\mathsf{x'' = \dfrac{5 - 3}{2} = \dfrac{2}{2} = 1}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{4\}}}}\leftarrow\textsf{letra C}$