Câu hỏi: Cho ${{4}^{x}}+{{4}^{-x}}=7$. Biểu thức $P=\dfrac{5+{{2}^{x}}+{{2}^{-x}}}{8-{{4.2}^{x}}-{{4.2}^{-x}}}$ có giá trị bằng
A. $P=\dfrac{3}{2}$.
B. $P=-\dfrac{5}{2}$.
C. $P=2$.
D. $P=-2$.
A. $P=\dfrac{3}{2}$.
B. $P=-\dfrac{5}{2}$.
C. $P=2$.
D. $P=-2$.
${{4}^{x}}+{{4}^{-x}}=7\Leftrightarrow {{\left( {{2}^{x}}+{{2}^{-x}} \right)}^{2}}=9\Leftrightarrow {{2}^{x}}+{{2}^{-x}}=3.$
Suy ra $P=\dfrac{5+{{2}^{x}}+{{2}^{-x}}}{8-{{4.2}^{x}}-{{4.2}^{-x}}}=\dfrac{5+3}{8-12}=-2.$
Suy ra $P=\dfrac{5+{{2}^{x}}+{{2}^{-x}}}{8-{{4.2}^{x}}-{{4.2}^{-x}}}=\dfrac{5+3}{8-12}=-2.$
Đáp án D.