设x+y=t
由x +2xy-1=0,得y=(1-x)/2x
t=x+(1-x)/2x
2x²-(2t+1)x+1=0
△=(-(2t+1))²-8>=0
2t+1>=2根号2,t>=(2根号2-1)/2
2t+1<=-2根号2,t<=(-2根号2-1)/2
x+y的取值范围是(-∞,(-2根号2-1)/2】∪【(2根号2-1)/2,+∞)
设x+y=t
由x +2xy-1=0,得y=(1-x)/2x
t=x+(1-x)/2x
2x²-(2t+1)x+1=0
△=(-(2t+1))²-8>=0
2t+1>=2根号2,t>=(2根号2-1)/2
2t+1<=-2根号2,t<=(-2根号2-1)/2
x+y的取值范围是(-∞,(-2根号2-1)/2】∪【(2根号2-1)/2,+∞)