Question

resolva a equação (n+2)! - (n+!)! = 25 sobre n(n-1)!

Answer 1

(n+2)(n+1)! - (n+1)! = 25/n(n-1)!

(n+2)(n+1)n(n-1)! - (n+1)n(n-1)! = 25/n(n-1)!

n(n-1)! . [(n+2)(n+1) - (n+1)] = 25/n(n-1)!

(n+2)(n+1) - (n+1) = 25

n²+n+2n+2-n-1 = 25

n²+2n+1-25=0

n²+2n-24=0

Δ = 2²-4.1.(-24)

Δ = 4+96

Δ = 100

 

n = (-2+/-√Δ)/2

n = (-2+/-\/100)/2

n = (-2+/-10)/2

n' = (-2+10)/2 = 4

n" = (-2-10)/2 = -6 (não convém)

 

S: n = 4