Question 1
Solve the system
$$\begin{cases}\dfrac1{\sqrt{1+2x^2}}+\dfrac1{\sqrt{1+2y^2}}=\dfrac2{\sqrt{1+2xy}},\\ \sqrt{x(1-2x)}+\sqrt{y(1-2y)}=\dfrac29.\end{cases}$$
$$\begin{cases}\dfrac1{\sqrt{1+2x^2}}+\dfrac1{\sqrt{1+2y^2}}=\dfrac2{\sqrt{1+2xy}},\\ \sqrt{x(1-2x)}+\sqrt{y(1-2y)}=\dfrac29.\end{cases}$$