Práctica 0 ejercicio 1m - versión 2017

EJERCICIO 1: Calcule

(m) $ \left(\dfrac{1}{4} - \left( \dfrac{2}{3} -\dfrac{1}{2} \right)^{2} \right)^{-2}$

Solución:

\begin{eqnarray*}
\left(\dfrac{1}{4} - \left( \dfrac{2}{3} -\dfrac{1}{2} \right)^{2} \right)^{-2} & = & \left(\dfrac{1}{4} - \left( \dfrac{4-3}{6} \right)^{2} \right)^{-2} \\
& = & \left(\dfrac{1}{4} - \left( \dfrac{1}{6} \right)^{2} \right)^{-2} \\
& = & \left(\dfrac{1}{4} - \left( \dfrac{1^{2}}{6^{2}} \right) \right)^{-2} \\
& = & \left(\dfrac{1}{4} - \left( \dfrac{1}{36} \right) \right)^{-2} \\
& = & \left(\dfrac{9-1}{36} \right)^{-2} \\
& = & \left(\dfrac{8}{36} \right)^{-2} \\
& = & \left(\dfrac{2}{9} \right)^{-2} \\
& = & \left(\dfrac{9}{2} \right)^{2} \\
& = & \dfrac{9^{2}}{2^{2}} \\
& = & \dfrac{81}{4} \\
\end{eqnarray*}

$$\boxed{ \left(\dfrac{1}{4} - \left( \dfrac{2}{3} -\dfrac{1}{2} \right)^{2} \right)^{-2} = \dfrac{81}{4} }$$