# Task 4. (12 points)

Solve the equation $x^{2}+y^{2}+1=x y+x+y$.

#
# Solution

$$
\begin{gathered}
x^{2}+y^{2}+1=x y+x+y \Leftrightarrow(x-y)^{2}+(x-1)^{2}+(y-1)^{2}=0 \Leftrightarrow \\
x=y=1 .
\end{gathered}
$$

Answer: $x=y=1$.