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Câu hỏi: Cho ${{9}^{x}}+{{9}^{-x}}=3$. Giá trị của biểu thức $T=\dfrac{15-{{81}^{x}}-{{81}^{-x}}}{3+\left| {{3}^{x}}-{{3}^{-x}} \right|}$ bằng bao nhiêu?
A. $T=2$
B. $T=3$
C. $T=4$
D. $T=1$
A. $T=2$
B. $T=3$
C. $T=4$
D. $T=1$
Ta có: ${{9}^{x}}+{{9}^{-x}}=3\Rightarrow \left\{ \begin{aligned}
& {{81}^{x}}+{{81}^{-x}}+2=9 \\
& {{({{3}^{x}}-{{3}^{-x}})}^{2}}+2=3 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& {{81}^{x}}+{{81}^{-x}}=7 \\
& \left| {{3}^{x}}-{{3}^{-x}} \right|=1 \\
\end{aligned} \right.$
Khi đó: $T=\dfrac{15-({{81}^{x}}+{{81}^{-x}})}{3+\left| {{3}^{x}}-{{3}^{-x}} \right|}=\dfrac{15-7}{3+1}=2$.
& {{81}^{x}}+{{81}^{-x}}+2=9 \\
& {{({{3}^{x}}-{{3}^{-x}})}^{2}}+2=3 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& {{81}^{x}}+{{81}^{-x}}=7 \\
& \left| {{3}^{x}}-{{3}^{-x}} \right|=1 \\
\end{aligned} \right.$
Khi đó: $T=\dfrac{15-({{81}^{x}}+{{81}^{-x}})}{3+\left| {{3}^{x}}-{{3}^{-x}} \right|}=\dfrac{15-7}{3+1}=2$.
Đáp án A.