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Câu hỏi: Phương trình ${{9}^{x}}-{{3.3}^{x}}+2=0$ có hai nghiệm ${{x}_{1}}$, ${{x}_{2}}$ $\left( {{x}_{1}}<{{x}_{2}} \right)$. Giá trị biểu thức $A=2{{x}_{1}}+3{{x}_{2}}$ là
A. $4{{\log }_{3}}2$.
B. 1.
C. $3{{\log }_{3}}2$.
D. $2{{\log }_{2}}3$.
A. $4{{\log }_{3}}2$.
B. 1.
C. $3{{\log }_{3}}2$.
D. $2{{\log }_{2}}3$.
Ta có: ${{9}^{x}}-{{3.3}^{x}}+2=0\Leftrightarrow \left[ \begin{aligned}
& {{3}^{x}}=1 \\
& {{3}^{x}}=2 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x=0 \\
& x={{\log }_{3}}2 \\
\end{aligned} \right.$.
Do $0<{{\log }_{3}}2\Rightarrow {{x}_{1}}=0$, ${{x}_{2}}={{\log }_{3}}2\Rightarrow A=2{{x}_{1}}+3{{x}_{2}}=2.0+3.{{\log }_{3}}2=3{{\log }_{3}}2$
& {{3}^{x}}=1 \\
& {{3}^{x}}=2 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x=0 \\
& x={{\log }_{3}}2 \\
\end{aligned} \right.$.
Do $0<{{\log }_{3}}2\Rightarrow {{x}_{1}}=0$, ${{x}_{2}}={{\log }_{3}}2\Rightarrow A=2{{x}_{1}}+3{{x}_{2}}=2.0+3.{{\log }_{3}}2=3{{\log }_{3}}2$
Đáp án C.