Question

Resolva as seguintes equações:
a) x! = 3(x-1)!
b) (n-3)! = 120
c) (x-2)! = 9 (x-3)!
d) (x-1)! = 12
(x-2)!

Answer 1

a) x! = 3(x-1)!           
x!/(x-1)! = 3         
x . (x-1)!/(x-1)! = 3      (a/a = 1, do mesmo modo (x-1)!/(x-1)! = 1)
x = 3 
_____________________________________
b) (n - 3)! = 120

120   1
120   2
60     3
20     4
5       5
1            120 = 5!
 
Voltando:
(n - 3)! = 120
(n - 3)! = 5!
n - 3 = 5
n = 5 + 3
n = 8
_______________________________
c) (x-2)! = 9 (x-3)!

(x-2)!/(x-3)! = 9
(x-2).(x-3)!/(x-3)! = 9       cortando:
x - 2 = 9
x = 11
________________________________
d)
(x-1)! = 12 (x-2)!
(x-1)!/(x-2)! = 12
(x-1).(x-2)!/(x-2)! = 12
x - 1 = 12
x = 12 + 1
x = 13

Bons estudos