Question

Resolva as equações a seguir:

A) (x-6)!/(x-5)!=1

B) (x-2)! . (x-1)!= 12 . (x-4)! . (x-1)!

C) (n+1)! - n!/ 7n = (n-1)!

Answer 1

Boa noite

A) (x-6)!/(x-5)!=1

1/(x - 5) = 1
x - 5 = 1
x = 6 

B) (x-2)! * (x-1)!= 12 * (x-4)! * (x-1)!

(x - 2)!/(x - 4)! = 12 
(x - 3)*(x - 2) = 12 
x^2 - 5x - 6 = 0
d^2 = 25 + 24 = 49
d = 7
x = (5 + 7)/2 = 6

C) (n+1)! - n!/ 7n = (n-1)!

(n +1)! - n! = 7n*(n-1)!

n = 7

8! - 7! = 7*7*6!

40320 - 5040 = 49*6! = 

35280 = 49*720
35280 = 35280