Đáp án:
$B$
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
{6.9^{\dfrac{1}{x}}} - {13.6^{\dfrac{1}{x}}} + {6.4^{\dfrac{1}{x}}} = 0\\
\Leftrightarrow 6.{\left( {{3^{\dfrac{1}{x}}}} \right)^2} - {13.3^{\dfrac{1}{x}}}{.2^{\dfrac{1}{x}}} + 6.{\left( {{2^{\dfrac{1}{x}}}} \right)^2} = 0\\
\Leftrightarrow 6.{\left( {{3^{\dfrac{1}{x}}}} \right)^2} - {9.3^{\dfrac{1}{x}}}{.2^{\dfrac{1}{x}}} - {4.3^{\dfrac{1}{x}}}{.2^{\dfrac{1}{x}}} + 6.{\left( {{2^{\dfrac{1}{x}}}} \right)^2} = 0\\
\Leftrightarrow \left( {{{2.3}^{\dfrac{1}{x}}} - {{3.2}^{\dfrac{1}{x}}}} \right)\left( {{{3.3}^{\dfrac{1}{x}}} - {{2.2}^{\dfrac{1}{x}}}} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{2.3^{\dfrac{1}{x}}} - {3.2^{\dfrac{1}{x}}} = 0\\
{3.3^{\dfrac{1}{x}}} - {2.2^{\dfrac{1}{x}}} = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
{\left( {\dfrac{3}{2}} \right)^{\dfrac{1}{x}}} = \dfrac{3}{2}\\
{\left( {\dfrac{3}{2}} \right)^{\dfrac{1}{x}}} = \dfrac{2}{3}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\dfrac{1}{x} = 1\\
\dfrac{1}{x} = - 1
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = - 1
\end{array} \right.
\end{array}$
Như vậy: Tích các nghiệm là $1.(-1)=-1$
Đáp án $B$
