Question

determine o valor de n nas equações (n+2)!+(n+1)!=15n!

Answer 1

(n+2)(n+1)!+(n+1)!= 15n!
(n+1)![(n+2)+1]=15n!
(n+1)(n)! [ n+3] =15n!
(n+1)(n+3)=15n!/n!
n^2 +4n +3 = 15
n^2 + 4n - 12=0
delta=16- 4. 1.-12
delta= 16 +48 = 64
n= (-4 +8)/2
n=2