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Determinați x € Z pentru care E(x)€ Z. E(x)=-6/x+4

Răspuns :

[tex] E(x) \in Z, \: E(x) = - \dfrac{6}{x+4} [/tex]

[tex] - \dfrac{6}{x + 4} \in \: Z \Longleftrightarrow x + 4 \in \mathcal{D}_{6} \Longleftrightarrow x + 4 \in \Big\{ \pm 1, \: \pm \: 2, \: \pm \: 3, \: \pm \: 6 \Big\} \: \Big|_{-4} \\ [/tex]

[tex] \Longrightarrow \boldsymbol {x \in \Big\{- 5, \: - 3, \: - 6, \: - 2, \: - 7, \: - 1, \: - 10, \: 2 \Big\}} \\[/tex]