Matematică
lorac
1

sa se rezolve exercițiul

+0
(1) Răspunsuri
poplucian1307

[latex]log_ {\dfrac{1}{3} } (x^2-4) \ \textgreater \ 0[\text]  [latex] \boxed{$ Conditii de existenta:$} \\ \\ \boxed{1} \quad x^2-4\ \textgreater \ 0 \Rightarrow x^2 \ \textgreater \ 4\Big| \sqrt{} \Rightarrow |x|\ \textgreater \ \sqrt{4} \Rightarrow |x|\ \textgreater \ 2 \\ \\ \Rightarrow x \ \textless \ -2 $ sau $ x\ \textgreater \ 2 \Rightarrow x\in(-\infty ,-2) \cup (2,\infty) \\ \\ \boxed{2} \quad x \neq 1 \\ \\ $Din \boxed{1} \cap $ $\boxed{2} \Rightarrow D =(-\infty ,-2) \cup (2,\infty)[/latex] [latex]\Rightarrow log_ {\dfrac{1}{3} } (x^2-4) \ \textgreater \ log_ {\dfrac{1}{3} } 1 \\ \\ \dfrac{1}{3}\ \textless \ 1 \Rightarrow $ functia logaritmica este strict descrescatoare$ \\ \\ \Rightarrow x^2-4\ \textless \ 1 \Rightarrow x^2\ \textless \ 5\Big| \sqrt{} \Rightarrow \sqrt{x^2}\ \textless \ \sqrt{5} \Rightarrow |x|\ \textless \ \sqrt{5} \Rightarrow \\ \\ \Rightarrow - \sqrt{5} \ \textless \ x \ \textless \ \sqrt{5} \Rightarrow {x\in\big(- \sqrt{5}, \sqrt{5}\big)} [/latex] [latex] \Rightarrow S = \big(- \sqrt{5}, \sqrt{5}\big) $ $ \cap $ $ D \Rightarrow S = \big(- \sqrt{5}, \sqrt{5}\big) $ $ \cap $ $ \Big[(-\infty ,-2) \cup (2,\infty)\Big] \Rightarrow \\ \\ \Rightarrow \boxed{S = \Big(- \sqrt{5},-2\Big)\cup \Big(2,\sqrt{5}\Big)}[/latex]

Adaugă răspuns