Question

Resolva a equação n! + 48/n! = 26​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{n! + \dfrac{48}{n!} = 26}$

$\sf{(n!)^2 - 26(n!) + 48 = 0}$

$\mathsf{y = n!}$

$\sf{y^2 - 26y + 48 = 0}$

$\sf{y^2 - 26y + 48 + 121 = 0 + 121}$

$\sf{y^2 - 26y + 169 = 121}$

$\sf{(y - 13)^2 = 121}$

$\sf{y - 13 = \pm\:\sqrt{121}}$

$\sf{y - 13 = \pm\:11}$

$\sf{y' = 11 + 13 = 24}$

$\sf{y'' = -11 + 13 = 2}$

$\mathsf{n! = 24 \Leftrightarrow n = 4}$

$\mathsf{n! = 2 \Leftrightarrow n = 2}$

$\boxed{\boxed{\mathsf{S = \{4;2\}}}}$