Question

Resolva a equação: (x - 1) ! / (x - 3) = 12

Answer 1

$\dfrac{(x-1)!}{(x-3)!}=12\Longrightarrow\dfrac{(x-1)(x-2)(x-3)!}{(x-3)!}=12\Longrightarrow (x-1)(x-2)=12\\\\ x^2-2x-x+2=12\Longrightarrow x^2-3x-10=0\\\\ \Delta=b^2-4\cdot a\cdot c\\ \Delta=(-3)^2-4\cdot1\cdot(-10)\\ \Delta=9+40\\ \Delta=49\\\\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{3\pm\sqrt{49}}{2\cdot1}=\dfrac{3\pm7}{2}\Longirghtarrow\begin{cases}x_1=\frac{3+7}{2}=\frac{10}{2}=5\\x_2=\frac{3-7}{2}=\frac{-4}{2}=-2\end{cases}\\\\ S=\{-2,5\}$

Answer 2

OBS: Provavelmente vc se esqueceu que em baixo também é fatorial, se não, não da pra resolver.

(x - 1) ! / (x - 3)! = 12
(x - 1) (x - 2)! / (x - 3)! = 12
(x - 1) (x - 2)(x - 3)! / (x - 3)! = 12
(x -1)(x - 2) = 12
x^2 -2x -x +2 = 12
x^2 -3x -10 = 0
Delta = 9 -4(1)(-10)
Delta = 9 +40
Delta = 49
x = (3 +- 7)/2
x' = (3 + 7)/2  = (10)/2 = 5
x'' = (3 - 7)/2 = -4/2 = -2
V = {-2,5}