若正数x,y满足x+3y=5xy,则3x+4y的最小值是(  )A.245B.285C.6D.

若正数x,y满足x+3y=5xy,则3x+4y的最小值是(  )A.245B.285C.6D.5
2025-05-20 22:06:00
推荐回答(1个)
回答1:

∵正数x,y满足x+3y=5xy,

x+3y
5xy
=1,即
1
5y
+
3
5x
=1,
∴3x+4y=(3x+4y)(
1
5y
+
3
5x

=
13
5
+
3x
5y
+
12y
5x
13
5
+2
3x
5y
?
12y
5x
=5
当且仅当
3x
5y
=
12y
5x
即x=1且y=
1
2
时取等号,
∴3x+4y的最小值为:5
故选:D