$PT \Leftrightarrow \left\{ \begin{array}{l} x+y=71-xy (1)\\ xy(x+y)=880 (2) \end{array} \right.$Thế (1) vào (2) $\Rightarrow x^2y^2-71xy+880=0$
$\Rightarrow xy=55$ hoặc $xy=16$
$* xy=55 \Rightarrow x+y=16 $
$\Rightarrow x^2+y^2=(x+y)^2-2xy=146$
$* xy=16 \Rightarrow x+y=55$
$\Rightarrow x^2+y^2=(x+y)^2-2xy=2993$