已知x,y,a,b∈R+,且ax+by=1,求x+y的最小值(  ) A.(a+b)2 B.1a+1b C.a+b D.a+b

问题描述:

已知x,y,a,b∈R+,且

a
x
+
b
y
=1,求x+y的最小值(  )
A. (
a
+
b
2
B.
1
a
+
1
b

C.
a
+
b

D. a+b

∵x,y,a,b∈R+,且

a
x
+
b
y
=1,
故x+y=(x+y)(
a
x
+
b
y
)=a+b+
ay
x
+
bx
y
≥a+b+2
ab
=(
a
+
b
2
故选A.