Tập nghiệm của bất phương trình 9^x-2(x+5)3^x+9(2x+1)>=0 là

* Hướng dẫn giải

Đáp án A

$$\begin{gathered} BPT\iff \left(3^x-2x-1\right)\left(3^x-9\right)\ge 0 \\ \iff \left[\begin{array}{l}\left\{\begin{array}{l}{3}^x\ge 2x+1\\ 3^x\ge 9\end{array}\right.\\ \left\{\begin{array}{l}{3}^x\le 2x+1\\ 3^x\le 9\end{array}\right.\end{array}\right.\iff \left[\begin{array}{l}\left\{\begin{array}{l}{3}^x\ge 2x+1\\ x\ge 2\end{array}\right.\\ \left\{\begin{array}{l}{3}^x\le 2x+1\\ x\le 2\end{array}\right.\end{array}\right.\left(1\right). \end{gathered}$$ 

$PT{3}^x=2x+1$ có hai nghiệm $x=0,x=1.$

Suy ra $\left(1\right)\iff \left[\begin{array}{l}\left\{\left[\begin{array}{l}x\ge 1\\ x\le 0\end{array}\right.\right.\\ \left\{\begin{array}{l}0\le x\le 1\\ x\le 2\end{array}\right.\end{array}\right.\iff \left[\begin{array}{l}x\ge 2\\ 0\le x\le 1\end{array}\right.\Rightarrow S=\left[0;1\right]\cup \left[2;+\infty \right).$