x<-1时,1-x^2<0,2x<0,不等式等价于1>1,舍-10,2x<0,不等式等价于(1-x^2)^2+1>1,等价于(1-x^2)^2>0,恒成立00,2x>0,不等式等价于(1-x^2)^2+1>(2x)^2+1等价于1-x^2>2x等价于x^2+2x-1<0等价于(x+1)^2<2,等价于-根号2x>1时,1-x^2<0,2x>0,不等式等价于1>(2x)^2+1等价于4x^2<0,舍显然x=-1,x=1时,不满足,x=0时满足,所以x的范围是(-1,根号2-1)
