[tex]\displaystyle\\
\left(\frac{9}{25}\right)^x -m\left(\frac{3}{5}\right)^x+1\ \textgreater \ 0~~~\text{Pentru oricare }~x\ \textless \ 0\\\\
\text{Inecuatia data este echivalenta cu urmatoarea inecuatie:}\\\\
\left(\frac{25}{9}\right)^x -m\left(\frac{5}{3}\right)^x+1\ \textgreater \ 0~~~\text{Pentru oricare }~x\ \textgreater \ 0\\\\
\left[\left(\frac{5}{3}\right)^2\right]^x -m\left(\frac{5}{3}\right)^x+1\ \textgreater \ 0~~~\text{Pentru oricare }~x\ \textgreater \ 0\\\\
[/tex]
[tex]\displaystyle\\
\left[\left(\frac{5}{3}\right)^x\right]^2 -m\left(\frac{5}{3}\right)^x+1\ \textgreater \ 0~~~\text{Pentru oricare }~x\ \textgreater \ 0\\\\
\text{Substitutie: }~~~\left(\frac{5}{3}\right)^x=y\\\\
y^2-my+1\ \textgreater \ 0 ~~~~~~\text{Pentru oricare }~y\ \textgreater \ 0\\\\
\text{Coeficientul lui y este pozitiv.}
\\ \text{Rezulta ca functia este pozitiva in afara radacinilor.}\\\\
\Delta = b^2-4ac =(- m)^2-4\cdot 1 = m^2-4\\
\Delta \ \textless \ 0\\
m^2-4\ \textless \ 0\\
m^2 \ \textless \ 4\\
m\ \textless \ 2\\
\boxed{\bf m \in (-\infty,~2)}
[/tex]
