When n= 1, x1= a.

Because x1-(√ a-1) = a-√ a+1= (√ a-0.5) 2+0.75 > 0.

So x1> √a- 1

When n≥2,

Xn =(Xn- 1+a/Xn- 1)/2≥√a & gt； √a- 1

To sum up, the original conclusion is established.