Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{A_{n,3} = 3(n - 1)}[/tex]
[tex]\mathsf{\dfrac{n!}{(n - 3)!} = 3(n - 1)}[/tex]
[tex]\mathsf{\dfrac{n.(n - 1).(n - 2).(n-3)!}{(n - 3)!} = 3(n - 1)}[/tex]
[tex]\mathsf{n.(n - 1).(n - 2) = 3(n - 1)}[/tex]
[tex]\mathsf{n.(n - 2) = 3}[/tex]
[tex]\mathsf{n^2 - 2n - 3 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-2)^2 - 4.1.(-3)}[/tex]
[tex]\mathsf{\Delta = 4 + 12}[/tex]
[tex]\mathsf{\Delta = 16}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{2 \pm \sqrt{16}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{2 + 4}{2} = \dfrac{6}{2} = 3}\\\\\mathsf{x'' = \dfrac{2 - 4}{2} = -\dfrac{2}{2} = -1}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{3\}}}}[/tex]
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Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{A_{n,3} = 3(n - 1)}[/tex]
[tex]\mathsf{\dfrac{n!}{(n - 3)!} = 3(n - 1)}[/tex]
[tex]\mathsf{\dfrac{n.(n - 1).(n - 2).(n-3)!}{(n - 3)!} = 3(n - 1)}[/tex]
[tex]\mathsf{n.(n - 1).(n - 2) = 3(n - 1)}[/tex]
[tex]\mathsf{n.(n - 2) = 3}[/tex]
[tex]\mathsf{n^2 - 2n - 3 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-2)^2 - 4.1.(-3)}[/tex]
[tex]\mathsf{\Delta = 4 + 12}[/tex]
[tex]\mathsf{\Delta = 16}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{2 \pm \sqrt{16}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{2 + 4}{2} = \dfrac{6}{2} = 3}\\\\\mathsf{x'' = \dfrac{2 - 4}{2} = -\dfrac{2}{2} = -1}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{3\}}}}[/tex]