The value of ‘a’ for which (a2-1)x2+2(a-1)x+2 is positive for any x are

We know that the expression ax2+bx+c>0 for all x,if a>0 and b2<4ac∴(a2-1)x2+2(a-1)x+2 is positive for all x ifa2-1>0 and 4(a-1)2-8(a2-1)<0⇒a2-1>0 and -4(a-1)(a+3)<0⇒a2-1>0 and (a-1)(a+3)>0⇒a2>1 and a<-3 or a>1     ⇒a<-3 or a>1