Solving an equation by telling the value of $x^2+y^2$. I have a problem solving an equation. The equation is:
$xy+x+y=44$ and $x^2y+xy^2=448$
and we have to tell the value of $x^2+y^2$
First I tried solving this by doing the following:
$xy+x+y=44~\to~x+y=44-xy~\to~x^2+2xy+y^2=44^2-88xy+x^2y^2~\Rightarrow$
$\Rightarrow~x^2+y^2=44^2-90xy+x^2y^2$
But from here I didn't know what to do. Could you help me in solving this equation?

$$xy+x+y=44$$
$$\implies xy+x+y+1=45=3\times15$$
$$\implies (y+1)(x+1)=3\times15$$
therefore $y=2$ and $x=14$ , also it satisfies the second identity. Hence $x^2+y^2=196+4=200.$
