Đáp án: `S={-3;-2}`
Giải thích các bước giải:
`2.4^{x+2} -5.6^{x+2} +3.9^{x+2}=0`
`<=> 2.4^x.4^2 - 5.6^x . 6^2 + 3.9^x. 9^2=0`
`<=> 32.4^x -180. 6^x + 243. 9^x=0`
`<=> 32. (2/3)^{2x} - 180. (2/3)^x +243=0`
Đặt `t= (2/3)^x` ta có:
`32. t² -180t +243=0`
`<=>` \(\left[ \begin{array}{l}t=\frac94\\t=\frac{27}{8}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}\Big(\frac23 \Big)^x = \frac94\\\Big(\frac23\Big)^x =\frac{27}{8}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=-2\\x=-3\end{array} \right.\)
Vậy `S={-3;-2}`
