Question

Se (n+4)! + (n+3)! = 15(n+2)!, Determine o(s) valor(es) de n.

Answer 1

(n+4)! + (n+3)! = 15(n+2)!
(n+4)! + (n+3)! ÷ (n+2)! = 15
(n+4)! ÷ (n+2)! + (n+3)! ÷ (n+2)! = 15
(n+4)(n+3)(n+2)! ÷ (n+2)! + (n+3)(n+2)! = 15
n²+7n+12+n+3=15
n²+8n+15-15=0
n²+8n=0
n(n+8)=0
n=0
n+8=0
n= -8

obs: (n+2)! ÷ (n+2)! corta dos dois lados