Question

calcule o n sabendo que :
(n-1)! (n+1)! = 72

Answer 1

$\frac{(n-1)!}{(n+1)!} = 72\\\\ \frac{(n-1)!}{(n+1)*(n-0)*(n-1)!} =72\\\\ \frac{1}{(n+1)*(n-0)} =72\\\\ \frac{1}{n^2+n}= 72\\\\1=72n^2+72n\\\\\boxed{0=72n^2+72n-1}}$

resolvendo por bhaskara
$n = \frac{-72\pm \sqrt{(72)^2-4*72*(-1)} }{2*72} \\\\\boxed{n = \frac{-72\pm \sqrt{5472} }{144} }$