Question

Resolva a equação:
(m+2)! m! - (m+1)! m! = 576

Answer 1

BOM DIA!

Para resolver esse problema não foi intuitivo para mim, porém eu após um tempo consegui resolver tal problema.

$(m+2)!m!-(m+1)!m!=576\\\\\frac{(m+2)!m!}{(m+1!)m!} - \frac{(m+1)!m!}{(m+1)!m!} = \frac{576}{(m+1)!m!} \\\\\frac{(m+2).(m+1)!}{(m+1!)} - 1 = \frac{576}{(m+1)!m!}\\\\m+2-1= \frac{576}{(m+1)!m!}\\\\m+1= \frac{576}{(m+1)!m!}\\\\m+1.(m+1)!= \frac{576}{m!}\\\\m+1.m+1.(m!)= \frac{576}{m!}\\\\(m+1)^2.m!.m!=576\\\\(m+1)^2.(m!)^2=576\\\\(m+1.m!)^2=576\\\\m+1.m!=\sqrt{576} \\\\m+1.m!=24\\\\(m+1)!=24\\\\m=3$

Bons estudos e abraços!