Cho \({4^x} + {4^{ - x}} =...

A

- Hướng dẫn giải

Ta có: \({4^x} + {4^{ - x}} = 23 \)

\(\Leftrightarrow {\left( {{2^x}} \right)^2} + {\left( {{2^{ - x}}} \right)^2} = 23 \\\Leftrightarrow {\left( {{2^x} + {2^{ - x}}} \right)^2} - {2.2^x}{.2^{ - x}} = 23 \\\Leftrightarrow {\left( {{2^x} + {2^{ - x}}} \right)^2} = 25 \\\Leftrightarrow {2^x} + {2^{ - x}} = 5\)

Khi đó \(K = \dfrac{{5 + 5}}{{1 - \left( 5 \right)}} = \dfrac{{10}}{{ - 4}} = - \dfrac{5}{2}\)