Question

(n+2)!/n!=20


calcule:
!=fatorial

Answer 1

vamos lá...

$\frac{(n+2)!}{n!} =20 \\ \\ \frac{(n+2)(n+1)\not n}{\not n}=20 \\ \\ (n+2)(n+1)=20 \\ \\ n^2+n+2n+2=20 \\ \\ n^2+3n+2-20=0 \\ \\ n^2+3n-18=0 \\ \\ \triangle=3^2-4(1)(-18) \\ \triangle=9+72 \\ \triangle=81 \\ \\ x= \frac{-3\pm \sqrt{81} }{2} = \frac{-3\pm9}{2} \\ \\ x'= \frac{-3+9}{2} = \frac{6}{2} =3 \\ \\ x"= \frac{-3-9}{2}=- \frac{12}{2}=-6~~ n/~~serve \\ \\ S=\{3\}$

Answer 2

Boa tarde Gui

(n + 2)!/n! = 20

(n + 2)*(n + 1)*n!/n! = 20

n² + 3n + 2 = 20
n² + 3n - 18 = 0

delta
d² = 9 + 72 = 81
d = 9

n = (-3 + 9)/2 = 3