若|2a-b|+(3b+2)=0求1/2(a-b)^2+1/4(2a+b)-1/3(a-b)^2+2a+b/2-(a-b)^2/6的值

题目

若|2a-b|+(3b+2)=0求1/2(a-b)^2+1/4(2a+b)-1/3(a-b)^2+2a+b/2-(a-b)^2/6的值

答案

|2a-b|+(3b+2)=0
∴2a-b=0
3b+2=0
∴a=-1/3
b=-2/3
(a-b)^2/2+(2a+b)/4-(a-b)^2/3+(2a+b)/2-(a-b)^2/6
=3(2a+b)/4
=3(-2/3-2/3)/4
=-1