Question

resolva a inequação exponencial
25^x+6.5^x +5>0

Answer 1

$25^x+6.5^x+5\ \textgreater \ 0 \\ 5^{2x}+6.5^x+5\ \textgreater \ 0 \\ Adotando{:}~5^x=a \\ a^2+6.a+5\ \textgreater \ 0 \\ \Delta=(6)^2-4(1)(5)=36-20=16 \Rightarrow \sqrt{\Delta} =4 \\ a'=(-6-4)/2(1)=-5 \\ a''=(-6+4)/2(1)=-1 \\ \\ a\ \textless \ -1~e~a\ \textgreater \ -5 \\ \\ Para~a\ \textgreater \ -5 \\ 5^x=a \Rightarrow 5^x\ \textgreater \ -5 \Rightarrow x\in \mathbb{R}~ |~ \forall~ x \\ Para~a\ \textless \ -1 \\ 5^x=a \Rightarrow 5^x\ \textless \ -1 \Rightarrow~ \notin~ x \\ \\ S=\{x\in \mathbb{R}~ |~ \forall~ x\}$