若正数x,y满足2x+y-3=0,则x+2yxy的最小值为( ) A.4 B.2 C.3 D.52
问题描述:
若正数x,y满足2x+y-3=0,则
的最小值为( )x+2y xy
A. 4
B. 2
C. 3
D.
5 2
答
∵正数x,y满足2x+y-3=0,∴3=2x+y.
∴
=x+2y xy
(2x+y)(1 3
+1 y
)=2 x
(5+1 3
+2x y
)≥2y x
(5+21 3
)=3,当且仅当x=y=1时取等号.
•2x y
2y x
则
的最小值为3.x+2y xy
故选:C.