已知函数y=lg[(a^2-1)x^2+(a+1)x+1]的值域为R,求实数a的取值范围?

解因为函数y=lg[(a^2-1)x^2+(a+1)x+1]的值域为R,所以(a^2-1)x^2+(a+1)x+1恒大于0,所以有方程(a^2-1)x^2+(a+1)x+1=0时△=（a+1）^2-4(a^2-1)＜0,解得a＞5/3,或a＜-1