x^2+2y+y√2=17-4√2
x,y为有理数
所以x^2+2y=17
y=-4
所以x^2=17-2y=25
x=5或x=-5
所以(x+y)(x+y)=(x+y)^2=(5-4)^2=1
或(x+y)(x+y)=(x+y)^2=(-5-4)^2=81