Question

Simplifique e calcule o valor de n: (Fatorial)
n! / (n-2)! =20

Answer 1

Oi Fran.

$\frac { n! }{ (n-2)! } =20\\ \\ \frac { n(n-1)(n-2)! }{ (n-2)! } =20\\ \\ n(n-1)=20\\ n^{ 2 }-n=20\\ n^{ 2 }-n-20=0\\ \\ (n-5)(n+4)=0\\ n-5=0\\ n=5\\ \\ n+4=0\\ n=-4\\ \\ S=\{ 5\}$