I4.4 Suppose that $\left(x_{0}, y_{0}\right)$ is a solution of the system: $\left\{\begin{array}{l}x y=6 \\ x^{2} y+x y^{2}+x+y+c=2\end{array}\right.$. Find the value of $d=x_{0}^{2}+y_{0}^{2}$.
From (2): $x y(x+y)+x+y-61=2$
$$
\begin{array}{l}
6(x+y)+(x+y)-63=0 \\
x+y=9 \\
d=x^{2}+y^{2}=(x+y)^{2}-2 x y=9^{2}-2 \times 6=69
\end{array}
$$