Đáp án:
\(\begin{array}{l}
34)\quad S = \{-1;2\}\\
35)\quad S = \{1\}\\
36)\quad S = \{-2;2\}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
34)\quad 12.9^x - 35.6^x + 18.4^x = 0\\
\Leftrightarrow 12.3^{2x} - 35.3^x.2^x + 18.2^{2x} = 0\\
\Leftrightarrow 12.\left(\dfrac32\right)^{2x} - 35.\left(\dfrac32\right)^x + 18 = 0\\
\Leftrightarrow \left[3\left(\dfrac32\right)^x - 2\right]\left[4\left(\dfrac32\right)^x - 9\right] =0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac32\right)^x = \dfrac23\\\left(\dfrac32\right)^x = \dfrac94\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac32\right)^x = \left(\dfrac32\right)^{-1}\\\left(\dfrac32\right)^x = \left(\dfrac32\right)^2\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = -1\\x = 2\end{array}\right.\\
\text{Vậy}\ S = \{-1;2\}\\
35)\quad 3.8^x + 4.12^x - 18^x - 2.27^x = 0\\
\Leftrightarrow 3.2^{3x} + 4.2^{2x}.3^x - 2^x.3^{2x} - 2.3^{3x} = 0\\
\Leftrightarrow \left(3.2^x - 2.3^x\right)\left(2^x + 3^x\right)^2 = 0\\
\Leftrightarrow \left[\begin{array}{l}3.2^x - 2.3^x = 0\\\left(2^x + 3^x\right)^2 = 0\quad (vn)\end{array}\right.\\
\Leftrightarrow 3.2^x = 2.3^x\\
\Leftrightarrow \left(\dfrac23\right)^x = \dfrac23\\
\Leftrightarrow x = 1\\
\text{Vậy}\ S = \{1\}\\
36)\quad \left(\sqrt{7 + \sqrt{48}}\right)^x + \left(\sqrt{7 - \sqrt{48}}\right)^x = 14\\
\Leftrightarrow \left(\sqrt{7 + \sqrt{48}}\right)^x + \dfrac{1}{\left(\sqrt{7 + \sqrt{48}}\right)^x} - 14= 0\\
\Leftrightarrow \left(\sqrt{7 + \sqrt{48}}\right)^{2x} - 14\left(\sqrt{7 + \sqrt{48}}\right)^x + 1=0\\
\Leftrightarrow \left[\begin{array}{l}\left(\sqrt{7 + \sqrt{48}}\right)^x = 7 + \sqrt{48}\\\left(\sqrt{7 + \sqrt{48}}\right)^x = 7 - \sqrt{48}\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = 2\\x = -2\end{array}\right.\\
\text{Vậy}\ S = \{-2;2\}\\
\end{array}\)
