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Câu hỏi: Nếu ${{\left( 7+4\sqrt{3} \right)}^{\alpha -1}}<7-4\sqrt{3}$ thì:
A. a < 1
B. a > 1
C. a > 0
D. a < 0
A. a < 1
B. a > 1
C. a > 0
D. a < 0
${{\left( 7+4\sqrt{3} \right)}^{a-1}}<7-4\sqrt{3}\Leftrightarrow {{\left( 7+4\sqrt{3} \right)}^{a-1}}<{{\left( 7+4\sqrt{3} \right)}^{-1}}$.
Mà $7+4\sqrt{3}>1$ nên ${{\left( 7+4\sqrt{3} \right)}^{a-1}}<{{\left( 7+4\sqrt{3} \right)}^{-1}}\Leftrightarrow a-1<-1\Leftrightarrow a<0$
Mà $7+4\sqrt{3}>1$ nên ${{\left( 7+4\sqrt{3} \right)}^{a-1}}<{{\left( 7+4\sqrt{3} \right)}^{-1}}\Leftrightarrow a-1<-1\Leftrightarrow a<0$
Đáp án D.