Question

(n+1)!
------- = 72
(n-1)!​

Answer 1

Resposta:

$\sf \dfrac{(n + 1)!}{(n -1)!} = 72$

$\sf \dfrac{(n + 1)n (n- 1)!}{(n -1)!} = 72 \quad \longleftarrow \mbox{cancela n fatorial iguais } }$

$\sf (n +1 ) n = 72$

$\sf n^2 + n - 72 = 0 \quad \longleftarrow \mbox{ Aplicar Bhaskara }$

$\sf n = \dfrac{-\,b \pm \sqrt{b^{2} -\, 4ac } }{2a} = \dfrac{-\,1 \pm \sqrt{1^{2} -\, 4\times 1 \times (-72) } }{2\times 1} = \dfrac{-\,1 \pm \sqrt{1 +288 } }{2}$

$\sf n = \dfrac{-\,1 \pm \sqrt{289 } }{2} = \dfrac{-\,1 \pm 17 }{2}$

$\sf n_1 = \dfrac{-\,1 + 17 }{2} = \dfrac{16 }{2} = 8$

$\sf n_2 = \dfrac{-\,1 - 17 }{2} = \dfrac{- 18 }{2} = - 9$    

 

O valor negativo serve, logo o valor para n = 8.

Explicação passo-a-passo: