VMO 2009 Problem 1

**Problem 1.**Find all $(x,y)$ such that: $$\{\begin{matrix} \dfrac {1}{\sqrt {1 + 2x^2}} + \dfrac {1}{\sqrt {1 + 2y^2}} & = & \dfrac {2}{\sqrt {1 + 2xy}} \sqrt {x(1 - 2x)} + \sqrt {y(1 - 2y)} & = & \dfrac {2}{9} \end{matrix}$$