Question

Sabendo Ax,2 =5.(x - 1)então x é:
a) 5
b) 6
c) 8
d) 2
e) 1​
me ajudem por favor, é urgente​

Answer 1

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$\boxed{\begin{array}{l}\sf A_{x,2}=5\cdot(x-1)\\\sf\dfrac{x!}{(x-2)!}=5\cdot(x-1)\\\sf\dfrac{x\cdot(x-1)\cdot\diagdown\!\!\!\!\!\!(x-\diagdown\!\!\!\!\!\!2)!}{\diagdown\!\!\!\!\!\!(x-\diagdown\!\!\!\!\!\!2)!}=5\cdot(x-1)\\\sf x\cdot(x-1)=5\cdot(x-1)\\\sf x^2-x=5x-5\\\sf x^2-x-5x+5=0\\\sf x^2-6x+5=0\\\sf s=6~~p=5\\\sf x_1=5~~x_2=1\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm verificac_{\!\!,}\tilde ao\!:}~\rm para~x=1:\\\sf A_{1,2}=\dfrac{1!}{(1-2)!}=\dfrac{1!}{-1!}\\\sf n\tilde ao~existe~fatorial~negativo.\\\sf portanto~x=1~n\tilde ao~\acute e~soluc_{\!\!,}\tilde ao.\\\sf para~x=5:\\\sf A_{5,2}=5\cdot(5-1)\\\sf A_{5,2}=5\cdot4=20\\\sf 5\cdot(5-1)=5\cdot4=20\\\sf logo~x=5~\acute e~soluc_{\!\!,}\tilde ao!\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$