Root number (x+y-3)+ root number (xy+4)=0.

So there are:

x+y-3=0

xy+4=0

x(3-x)+4=0

-x^2+3x+4=0

x^2-3x-4=0

(x-4)(x+ 1)=0

Solution: x 1=4, x2=- 1.

y 1=- 1，y2=4

Therefore, x2+y2 =16+1=17.