Question

Questão sobre fatorial: se n!/2!(n-2)! = 28, então n vale:

a)7
b)8
c)1
d)26
e)56

Answer 1

n!/2!(n - 2)! = 28
n . (n - 1) . (n - 2)!/2! (n - 2)! = 28
n² - n/2 = 28
n² - n = 28 . 2
n² - n = 56
n² - n - 56 = 0
a = 1, b = - 1, c = - 56

Δ = b² - 4ac
Δ = (- 1)² - 4 . 1 . (- 56)
Δ = 1 + 224
Δ = 225

n = (- b ± √Δ)/2a
n = (- (- 1) ± √225)/2 . 1
n = (1 ± 15)/2

n' = (1 + 15)/2 = 16/2 = 8
n'' = (1 - 15)/2 = - 14/2 = - 7

n = 8, n = - 7

Descarta o - 7.

Resposta: Letra b) 8