Question

03-Simplifique as expressões: a) 7!/9! = b) 3!8!/2!6!= c) 4!+6!/6! = d) 5!-3!/3! = e) (n+1)!/n! = f) x!/(x-2) =2 Preciso urgenteeeee com a resoluçãoooo!!!

Answer 1

Resposta:

Explicação passo-a-passo:

a) 7!/9! = 7!/9.8.7! = 1/9.8 = 1/72.

b) 3!8!/2!6! = 3.2!8.7.6!/2!6! = 3.8.7 = 168.

c) (4! + 6!)/6! = (4! + 6.5.4!)/6.5.4! =  (1 + 6.5).4!/6.5.4! = (1 + 30)/30 = 31/30.

d) (5! - 3!)/3! = (5.4.3! - 3!)/3! = (5.4 - 1)3!/3! = (20 - 1) = 19.

e) (n + 1)!/n! = (n + 1) . n!/n! = n + 1.

f) x!/(x - 2)! = 2

x . (x – 1) . (x – 2)!/(x - 2)! = 2

x . (x – 1) = 2

x² - x = 2

x² - x - 2 = 0

Δ = b² - 4ac

Δ = (-1)² - 4(1)(-2)

Δ = 1 + 8 = 9

x = (- b ± √Δ)/2a

x =  (- (-1) ± √9)/2(1)

x = ( 1 ± 3)/2

x = (1 + 3)/2

x = 4/2

x = 2.

x = (1 - 3)/2

x = - 2/2

x =  - 1.