Question

No puedo terminarlo.. Ayuda.. ​

Answer 1

Resolviendo y hallando el valor de X:

${4}^{x + 2} + {4}^{x + 4} + {4}^{x + 5} - 81 = 0 \\ {2}^{2(x + 2)} + {2}^{2(x + 4)} + {2}^{2(x + 5)} = 81 \\ {2}^{2x + 4} + {2}^{2x + 8} + {2}^{2x + 10} = 81 \\ {2}^{2x + 4} (1 + {2}^{4} + {2}^{6} ) = 81 \\ {2}^{2x + 4} (1 + 16 + 64) = 81 \\ {2}^{2x + 4} (81) = 81 \\ {2}^{2x + 4} = 1 \\ {2}^{2x + 4} = {2}^{0} \\ \\ \\ 2x + 4 = 0 \\ 2x = - 4 \\ x = \frac{ - 4}{2} \\ x = - 2$

Hallando lo que te piden :

$x + {x}^{ - 1} = x + \frac{1}{x} = ( - 2) + \frac{1}{ ( - 2)} = \frac{ 2 \times ( - 2)}{2 \times 1} - \frac{1}{2} = \frac{ - 4}{2} - \frac{1}{2} = \frac{ - 4 - 1}{2} = \frac{ - 5}{2}$

Respuesta : B) -5/2