tập nghiệm của phương trình (1/3)^2/x +3.(1/3)^(1/x+1)>12

Giải thích các bước giải:

 ĐKXĐ: x$ \ne $0

$\begin{gathered}   {\frac{1}{3}^{\frac{2}{x}}} + 3.{\frac{1}{3}^{\frac{1}{x} + 1}} > 12 \hfill \\    \Leftrightarrow {({\frac{1}{3}^{\frac{1}{x}}})^2} + 3.\frac{1}{3}.{\frac{1}{3}^{\frac{1}{x}}} > 12 \hfill \\    \Leftrightarrow {({\frac{1}{3}^{\frac{1}{x}}})^2} + {\frac{1}{3}^{\frac{1}{x}}} - 12 > 0 \hfill \\    \Leftrightarrow ({\frac{1}{3}^{\frac{1}{x}}} + 4)({\frac{1}{3}^{\frac{1}{x}}} - 3) > 0 \hfill \\    \Leftrightarrow \left[ \begin{gathered}   {\frac{1}{3}^{\frac{1}{x}}} + 4 > 0 \hfill \\   {\frac{1}{3}^{\frac{1}{x}}} - 3 < 0 \hfill \\  \end{gathered}  \right.(do\,{\frac{1}{3}^{\frac{1}{x}}} + 4 > {\frac{1}{3}^{\frac{1}{x}}} - 3\forall tm\,DKXD) \hfill \\    \Leftrightarrow \left[ \begin{gathered}   {\frac{1}{3}^{\frac{1}{x}}} - 3 > 0 \hfill \\   {\frac{1}{3}^{\frac{1}{x}}} + 4 < 0(vo\,li\,do{\frac{1}{3}^{\frac{1}{x}}} > 0\forall x\,tm\,DKXD)\, \hfill \\  \end{gathered}  \right. \hfill \\    \Leftrightarrow {\frac{1}{3}^{\frac{1}{x}}} > 3 \hfill \\    \Leftrightarrow {\frac{1}{3}^{\frac{1}{x}}} > {\frac{1}{3}^{ - 1}} \hfill \\    \Leftrightarrow \frac{1}{x} <  - 1(do\,\frac{1}{3} < 1) \hfill \\    \Leftrightarrow \frac{1}{x} + 1 < 0 \hfill \\    \Leftrightarrow \frac{{1 + x}}{x} < 0 \hfill \\    \Leftrightarrow \left\{ \begin{gathered}   1 + x > 0 \hfill \\   x < 0 \hfill \\  \end{gathered}  \right.(do\,1 + x > x) \hfill \\    \Leftrightarrow \left\{ \begin{gathered}   x >  - 1 \hfill \\   x < 0 \hfill \\  \end{gathered}  \right. \hfill \\    \Leftrightarrow  - 1 < x < 0 \hfill \\  \end{gathered} $