问题
填空题
若正数x,y满足x+3y=5xy,则3x+4y的最小值是______.
答案
∵x+3y=5xy,x>0,y>0
∴
+1 5y
=13 5x
∴3x+4y=(3x+4y)(
+1 5y
)=3 5x
+13 5
+3x 5y
×3≥4y 5x
+213 5
=5
?3x 5y 12y 5x
当且仅当
=3x 5y
即x=2y=1时取等号12y 5x
故答案为:5
若正数x,y满足x+3y=5xy,则3x+4y的最小值是______.
∵x+3y=5xy,x>0,y>0
∴
+1 5y
=13 5x
∴3x+4y=(3x+4y)(
+1 5y
)=3 5x
+13 5
+3x 5y
×3≥4y 5x
+213 5
=5
?3x 5y 12y 5x
当且仅当
=3x 5y
即x=2y=1时取等号12y 5x
故答案为:5