Question

Se (x+4)! + (x+3)! = 15 (x+2)! Qual o valor de x?

Answer 1

Explicação passo-a-passo:

$\sf (x+4)!+(x+3)!=15\cdot(x+2)!$

$\sf (x+4)\cdot(x+3)\cdot(x+2)!+(x+3)\cdot(x+2)!=15\cdot(x+2)!$

$\sf (x+2)!\cdot[(x+4)\cdot(x+3)+(x+3)]=15\cdot(x+2)!$

$\sf (x+4)\cdot(x+3)+(x+3)=15$

$\sf x^2+3x+4x+12+x+3-15=0$

$\sf x^2+8x=0$

$\sf x\cdot(x+8)=0$

$\sf x'=0$

$\sf x+8=0~\rightarrow~x"=-8$ (não serve)

$\sf S=\{0\}$