Question

Resolva a equação
(n+2)!+(n+1)!=15n!

Answer 1

(n+2)!+(n+1)!=15n!
(n+2)(n+1)n!+(n+1)n!=15n!
(n+2)(n+1)+n+1=15
n²+3n+2+n+1=15
n²+4n-12=0

Δ=(-4)²-4.1.(-12)
Δ=16+48
Δ=64

$n=\frac{-4 + \sqrt{64}}{2}=\frac{-4+8}{2}=\frac{4}{2}=2$