Question

What is the value of x is equals to root 6 + root 6 + root 6 + root 6 upto infinity?

Answer 1

Let us assume : x= root(6+root(6 + root(6 + ………

So,

x= root(6+x)

x^2=6+x

x^2-x-6=0

(x-3)(x+2)=0

So, x=3 or -2.

x is positive ie root 6 + root 6 + root 6 + root 6 upto infinity is positive
then we discard x=-2

So the answer is x =3.