Đáp án:
\(S = \{4\}\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad 4.3^x - 9.2^x = 5.6^{\tfrac x2}\\
\Leftrightarrow 4.\left(3^{\tfrac x2}\right)^2 - 5.3^{\tfrac x2}.2^{\tfrac x2} - 9.\left(2^{\tfrac x2}\right)^2 = 0\\
\Leftrightarrow 4.\left(\dfrac32^{\tfrac x2}\right)^2 - 5.\left(\dfrac32^{\tfrac x2}\right) - 9 = 0\\
\Leftrightarrow \left[\left(\dfrac32^{\tfrac x2}\right) + 1\right]\left[4\left(\dfrac32^{\tfrac x2}\right) - 9\right] = 0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac32\right)^{\tfrac x2} = -1\quad (vn)\\\left(\dfrac32\right)^{\tfrac x2} = \dfrac94\end{array}\right.\\
\Leftrightarrow \dfrac{x}{2} = 2\\
\Leftrightarrow x = 4\\
\text{Vậy}\ S = \{4\}
\end{array}\)
