`(sqrt(31+sqrt(31+sqrt(31+...))))/(sqrt(1+sqrt(1+sqrt(1+...))))=a-sqrt(b)` where `a, b in N` then find the value of `a+b`.

(sqrt(31) - sqrt(29))/(sqrt(31) + sqrt(29)) equals:

(sqrt(5)-1)/(sqrt(5)+1)+(sqrt(5)+1)/(sqrt(5)-1) =a+b sqrt(5) Then find the value of a and b

(sqrt(7)+1)/(sqrt(7)-1)-(sqrt(7)-1)/(sqrt(7)+1)=a+b sqrt(7)

(sqrt(5)-1)/(sqrt(5)+1)+(sqrt(5)+1)/(sqrt(5)-1)=a+b sqrt(5)

Let S=(sqrt(1))/(1+sqrt1+sqrt(2))+sqrt(2)/(1+sqrt(2)+sqrt(3))+(sqrt(3))/(1+sqrt(3)+sqrt(4))+...+(sqrt(n))/(1+sqrt(n)+(sqrtn+1))=10 Then find the value of n.

Let S=(sqrt(1))/(1+sqrt1+sqrt(2))+sqrt(2)/(1+sqrt(2)+sqrt(3))+(sqrt(3))/(1+sqrt(3)+sqrt(4))+...+(sqrt(n))/(1+sqrt(n)+(sqrtn+1))=10 Then find the value of n.

Let S=(sqrt(1))/(1+sqrt1+sqrt(2))+sqrt(2)/(1+sqrt(2)+sqrt(3))+(sqrt(3))/(1+sqrt(3)+sqrt(4))+...+(sqrt(n))/(1+sqrt(n)+(sqrtn+1))=10 Then find the value of n.

If 2(sqrt(3+sqrt(5-sqrt(13+sqrt(48)))))=sqrt(a)+sqrt(b) where a and b are nutural number find (a+b).

If a=(sqrt(2)+1)/(sqrt(2)-1) and b=(sqrt(2)-1)/(sqrt(2)+1) ,then find the value of a^(2)+b^(2)-4ab