Question

resolva a equação: (x+4)! + (x+3)! = (x+2)! . 15

Answer 1

(x+4)!+(x+3)! = (x+2)!.15
(x+4)(x+3)(x+2)! +(x+3)(x+2)!=(x+2)!15
(x+2)! . ((x+4).(x+3)+(x+3))=(x+2)!15
(x+4).(x+3)+(x+3) =(x+2)!15 / (x+2)!
(x+4).(x+3)+(x+3) =15

x²+7x+12+x+3=15
x²+8x= 0

x(x+8) =

x=0
ou
 x+8=0  x=-8

solusção x=0
 

Answer 2

$

Ola Maah

(x + 4)! + (x + 3)! = 15*(x + 2)!

(x + 4)! + (x + 3)!  = 15*(x + 2)!

(x + 4)*(x + 3)(x + 2)! + (x + 3)*(x + 2)! = 15*(x + 2)!

(x + 3)*(x + 5) = 15

x² + 8x + 15 = 18

x² + 8x = 0

x(x + 8) = 0

x1 = 0
x2 = -8 (não serve)

4! + 3! = 15*2!

24 + 6 = 15*2 

30 = 30 ok

pronto