Question

Equação fatorial Me ajuda a responder!
$\frac{(n -2)!}{(n -4)!} =2$

Answer 1

Resposta:

$\frac{(n - 2)!}{(n - 4)!} = 2$

$\frac{(n - 2) \times (n - 3) \times (n - 4)!}{(n - 4)!} = 2$

REDUZA A FRAÇÃO

$(n - 2) \times (n - 3) = 2$

${n}^{2} - 3n - 2n + 6 = 2$

${n}^{2} - 5n + 6 = 2$

${n}^{2} - 5n + 6 - 2 = 0$

${n}^{2} - n - 4n + 4 = 0$

$n \times (n - 1) - 4(n - 1) = 0$

$(n - 1) \times (n - 4) = 0$

$n - 1 = 0$

$n - 4 = 0$

$n = 1$

$n = 4$

$\frac{(1 - 2)!}{(1 - 4)!} = 2$

$\frac{(4 - 2)!}{(4 - 4)!} = 2$

$\frac{( - 1)!}{(1 - 4)!} = 2$

$2 = 2$

$n≠1$

$n = 4$

$n = 4$

ATT:ARMANDO