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

x+2y
xy
的最小值为(  )
A. 4
B. 2
C. 3
D.
5
2

∵正数x,y满足2x+y-3=0,∴3=2x+y.

x+2y
xy
=
1
3
(2x+y)(
1
y
+
2
x
)
=
1
3
(5+
2x
y
+
2y
x
)
1
3
(5+2
2x
y
2y
x
)
=3,当且仅当x=y=1时取等号.
x+2y
xy
的最小值为3.
故选:C.