若4x2+9y2-4x-12y+5=0,则2x+3/2y=_.

问题描述:

若4x2+9y2-4x-12y+5=0,则2x+

3
2
y=______.

∵4x2+9y2-4x-12y+5=(4x2-4x+1)+(9y2-12y+4)=(2x-1)2+(3y-2)2=0,
∴2x-1=0且3y-2=0,
解得:x=

1
2
,y=
2
3

则2x+
3
2
y=2×
1
2
+
3
2
×
2
3
=1+1=2.
故答案为:2