Question

(n+5)! +(n+4)! =35 (N+3)!

Answer 1

(n+5).(n+4).(n+3)! + (n+4).(n+3)! = 35.(n+3)!
(n+4).(n+5+1) = 35
(n+4).(n+6) = 35
n² + 10n + 24 - 35 = 0
n² + 10n - 11 = 0
/\ = 10² - 4.1.(-11)
/\ = 100 + 44
/\ = 144
n = (-10+/- \/144)/2
n = (-10+/-12)/2
n' = (-10+12)/2 = 2/2 = 1
n" = (-10-12)/2 = -22/2 = -11 (não convém)
Resposta: n = 1