(1)a^2(x-1)+a(x+3)<6x+2(a^2+a-6)x<a^2-3a+2(a+3)(a-2)x<(a-1)(a-2)当a-2=0时,无解当a-2≠0即a≠2时原不等式<=>(a+3)x<a-1当a+3>0,即a>-3且a≠2时,x<(a-1)/(a+3)当a+3<0,即a<-3时,x>(a-1)/(a+3)(2)当 展开
(1)a^2(x-1)+a(x+3)<6x+2(a^2+a-6)x<a^2-3a+2(a+3)(a-2)x<(a-1)(a-2)当a-2=0时,无解当a-2≠0即a≠2时原不等式<=>(a+3)x<a-1当a+3>0,即a>-3且a≠2时,x<(a-1)/(a+3)当a+3<0,即a<-3时,x>(a-1)/(a+3)(2)当a>-3时,使x=0在上述不等式的解集中,则(a-1)/(a+3)>0,得a>1且a≠2当a<-3时使x=0在上述不等式的解集中,则(a-1)/(a+3)<0无解.所以a的取值范围是(1,2)∪(2,+∞) 收起
