Question

(matemática)
Resolver a equação (n+2)!+(n+1)!=15.n!

Answer 1

(n+2)!+(n+1)!=15.n!
(n+2).(n+1).n! + (n+1).n! = 15.n!
[(n+2).(n+1) + (n+1)].n! = 15.n!
[n²+n+2n+2+(n+1)].n! = 15.n!
[n²+3n+2+n+1].n!/n! = 15
n²+4n+3 = 15
n²+4n+3-15 = 0
n²+4n-12 = 0

a = 1 ; b = 4 ; c = -12

∆ = b² - 4.a.c
∆ = 4²-4.1.(-12)
∆ = 16+48
∆ = 64

n = [-b±√∆]/2.a
n = [-4±√64]/2.1
n = [-4±8]/2

n' = [-4-8]/2
n' = -12/2

n' = -6

n" = [-4+8]/2

n" = 4/2

n" = 2

S{-6, 2}



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