<s>[INST] Solve the system $ \left\lbrace \begin{array}{ccc} \sqrt{1-x} + \sqrt{1-y} &=& \frac{y-x}{2} \\ x+y &=& 2xy \end{array}\right. $ I have to solve the following system:
$$
\left\lbrace \begin{array}{ccc}
\sqrt{1-x} + \sqrt{1-y} &=& \frac{y-x}{2} \\
x+y  &=& 2xy
\end{array}\right.
$$
I've showed that it is equivalent to
$$
\left\lbrace \begin{array}{ccc}
 \sqrt{1-x} - \sqrt{1-y} &=& 2 \\
 x+y  &=& 2xy
\end{array}\right. \text{ or } x=y= 1
$$
And i can't conclude nothing frome this system:
$$
\left\lbrace \begin{array}{ccc}
 \sqrt{1-x} - \sqrt{1-y} &=& 2 \\
 x+y  &=& 2xy
\end{array}\right.
$$
 [/INST] $$
\left\lbrace \begin{array}{ccc}
 \sqrt{1-x} - \sqrt{1-y} &=& 2 &(1)\\
 x+y  &=& 2xy &(2)
\end{array}\right.
$$
From 1, get squared both sides two times, replace all (x + y) by 2xy, you will recieve a equation of (xy).
Find the appropriate of (xy) and then solve the (2) equation.
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