设x>0,y>0,x+y+xy=2,则x+y的最小值是(  ) A.32 B.1+3 C.23-2 D.2-3

问题描述:

设x>0,y>0,x+y+xy=2,则x+y的最小值是(  )
A.

3
2

B. 1+
3

C. 2
3
-2
D. 2-
3

∵x>0,y>0,∴x+y≥2xy(当且仅当x=y时取等号),则xy≤x+y2,xy≤(x+y)24,∵x+y+xy=2,∴xy=-(x+y)+2≤(x+y)24,设t=x+y,则t>0,代入上式得,t2+4t-8≥0,解得,t≤-2-23或t≥23-2,则t≥23-2,故x+y的最小...