Prove :

If:$\displaystyle \left\{ \begin{array}{l}

x,y \in \Re+ \\

n \in {\rm N} \\

x + y = 1 \\

\end{array} \right.

$

Then:$\displaystyle \left( {1 + \frac{1}{{x^n }}} \right)\left( {1 + \frac{1}{{y^n }}} \right) \ge \left( {1 + 2^n } \right)^2

$