Question 140974
xy + x + y = 71
x^2y + xy^2 = 880

using 2nd eq then xy(x+y)=880
then using 1st eq xy(71-xy)=880

let w=xy then  -w^2+71w-880=0

xy=16 or xy=55
and
x+y=55 or x+y=16



case 1)xy=16 and x+y=55 (is not possible) because x and y positive integers
case 2)xy=55 and x+y=16 (x=11,y=5 or x=5,y=11)
x^2+y^2= (x+y)^2-2xy = 16^2-2(55)=146

Answer: x^2+y^2=146