Question

Calcule o valor de n nas expressões:
a) (n+2)!=6n!

Answer 1

(n + 2)! = 6.n!

(n + 2)(n + 1)n! = 6n!

(n + 2)(n + 1) = 6

n² + n + 2n + 2 - 6 = 0

n² + 3n - 4 = 0

∆ = b² - 4ac
∆ = 3² - 4.1.(- 4)
∆ = 9 + 16
∆ = 25

x = -b±√∆ /2a
x = -3±√25 /2.1
x = -3±5 /2

x' = -3+5 /2
x' = 2/2
x' = 1

x" = - 3 - 5 /2
x" = - 8/2
x" = - 4 (nao convem)

R.: n = 1