关于x的不等式|x-[(a+1)^2]/2|<=(a-1)^2/2与x^2-3(a+1)x+2(3a+1)<=0(a属于R)的解集分别为A和B,求```

|x-[(a+1)^2]/2|<=(a-1)^2/2
[x-(a+1)^2/2]^2<=[(a-1)^2/2]^2
(x-a)[2x-(a^2+1)]<=0
x1=a x2=(a^2+1)/2
如果(a^2+1)/2>a即a不为1 A={x|a<=x<=(a^2+1)/2}
如果(a^2+1)/2<a即a为空集 A={x|(a^2+1)/2<=x<=a}
如果(a^2+1)/2=a即a=1 A为空集
所以a=1时 A为空集 A不等于1时 A={x|a<=x<=(a^2+1)/2}

x^2-3(a+1)x+2(3a+1)<=0
(x-2)[x-(3a+1)]<=0
x1=2 x2=3a+1
如果3a+1>2即a>1/3 B={x|2<=x<=3a+1}
如果3a+1<2即a<1/3 B={x|3a+1<=x<=2}
如果3a+1=2即a=1/3 B为空集

讨论
当a>1/3且a不等于1时
A={x|a<=x<=(a^2+1)/2} B{x|2<=x<=3a+1}
a>=2
(a^2+1)/2<=3a+1
解得 2<=a<=3+根号5
当a<1/3时
A={x|a<=x<=(a^2+1)/2} B={x|3a+1<=x<=2}
a>=3a+1
(a^2+1)/2<=2
解得 -根号3<=a<=-1/2
当a=1/3时 B为空集 a无解
当a=1时 A为空集 a为全体实数
所以
a的取值范围为[-根号3，-1/2]U[2,3+根号5]或者a=1

A<B+a