lorac
1

# sa se rezolve exercițiul

(1) Răspunsuri
poplucian1307

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