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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 $A=2{{x}_{1}}+3{{x}_{2}}$ thuộc
A. $\left[ 2;+\infty \right).$
B. $\left[ -2;1 \right].$
C. $\left[ \dfrac{1}{4};2 \right].$
D. $\left( -\infty ;\dfrac{1}{4} \right].$
${{9}^{x}}-{{3.3}^{x}}+2=0\Leftrightarrow {{\left( {{3}^{x}} \right)}^{2}}-{{3.3}^{x}}+2=0\Leftrightarrow \left[ \begin{aligned}
& {{3}^{x}}=2 \\
& {{3}^{x}}=1 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x={{\log }_{3}}2 \\
& x=0 \\
\end{aligned} \right.$.
Suy ra: ${{x}_{1}}=0; {{x}_{2}}={{\log }_{3}}2$
Vậy $A=2{{x}_{1}}+3{{x}_{2}}=2.0+3.{{\log }_{3}}2=3{{\log }_{3}}2$
A. $\left[ 2;+\infty \right).$
B. $\left[ -2;1 \right].$
C. $\left[ \dfrac{1}{4};2 \right].$
D. $\left( -\infty ;\dfrac{1}{4} \right].$
${{9}^{x}}-{{3.3}^{x}}+2=0\Leftrightarrow {{\left( {{3}^{x}} \right)}^{2}}-{{3.3}^{x}}+2=0\Leftrightarrow \left[ \begin{aligned}
& {{3}^{x}}=2 \\
& {{3}^{x}}=1 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x={{\log }_{3}}2 \\
& x=0 \\
\end{aligned} \right.$.
Suy ra: ${{x}_{1}}=0; {{x}_{2}}={{\log }_{3}}2$
Vậy $A=2{{x}_{1}}+3{{x}_{2}}=2.0+3.{{\log }_{3}}2=3{{\log }_{3}}2$
Đáp án C.