Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{n(h) = h^2 + h + 1}[/tex]
[tex]\mathsf{h^2 + h + 1 = 57}[/tex]
[tex]\mathsf{h^2 + h - 56 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = 1^2 - 4.1.(-56)}[/tex]
[tex]\mathsf{\Delta = 1 + 224}[/tex]
[tex]\mathsf{\Delta = 225}[/tex]
[tex]\mathsf{h = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-1 \pm \sqrt{225}}{2} \rightarrow \begin{cases}\mathsf{h' = \dfrac{-1 + 15}{2} = \dfrac{14}{2} = 7}\\\\\mathsf{h'' = \dfrac{-1 - 15}{2} = -\dfrac{16}{2} = -8}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{7\}}}}\leftarrow\textsf{letra A}[/tex]
