\(x^2y+xy^2+x+y=63\Leftrightarrow xy\left(x+y\right)+\left(x+y\right)=63\Leftrightarrow\left(x+y\right)\left(xy+1\right)=63\Leftrightarrow\left(6+1\right)\left(x+y\right)=63\Leftrightarrow x+y=9\\ \\x^2+y^2=\left(x+y\right)^2-2xy=9^2-2.6=69\)
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