Đáp án:
\(\begin{array}{l}
9)\,\,\,\left[ \begin{array}{l}
x = 1\\
x = - 1
\end{array} \right.\\
10)\,\,\left[ \begin{array}{l}
x = 0\\
x = 2
\end{array} \right.\\
11)\,\,\,x = - 2.
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
9)\,\,\,{3^{1 + x}} + {3^{1 - x}} = 10\\
\Leftrightarrow {3.3^x} + \frac{3}{{{3^x}}} - 10 = 0\\
\Leftrightarrow {3.3^{2x}} - {10.3^x} + 3 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{3^x} = 3\\
{3^x} = \frac{1}{3}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = - 1
\end{array} \right..\\
10)\,\,\,{3^x} + {3^{2 - x}} = 10\\
\Leftrightarrow {3^x} + \frac{{{3^2}}}{{{3^x}}} - 10 = 0\\
\Leftrightarrow {3^{2x}} - {10.3^x} + 9 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{3^x} = 1\\
{3^x} = 9
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 2
\end{array} \right..\\
11)\,\,\,{3^{2x + 4}} + {45.6^x} - {9.2^{2x + 2}} = 0\\
\Leftrightarrow {3^4}{.3^{2x}} + {45.3^x}{.2^x} - {9.2^2}{.2^{2x}} = 0\\
\Leftrightarrow {81.3^{2x}} + {45.3^x}{.2^x} - {36.2^{2x}} = 0\\
\Leftrightarrow 81.{\left( {\frac{3}{2}} \right)^{2x}} + 45.{\left( {\frac{3}{2}} \right)^x} - 36 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{\left( {\frac{3}{2}} \right)^x} = \frac{4}{9} = {\left( {\frac{2}{3}} \right)^2}\\
{\left( {\frac{3}{2}} \right)^x} = - 1\,\,\,\left( {ktm} \right)
\end{array} \right.\\
\Leftrightarrow x = - 2.
\end{array}\)
