Answer Posted / soundararajan krishnan

I think the actual question may be like
sqrt(x+sqrt(x+sqrt(x+sqrt(x+...))))=2;
Find the value of x?

When we solve this the value of x is 2.

Let A = sqrt(x+sqrt(x+sqrt(x+sqrt(x+...)))) ------(1)
We can write this as,

A = sqrt (x+A) ------(2) using formula (1)

Since A = sqrt(x+sqrt(x+sqrt(x+sqrt(x+...)))) = 2,

we can write the equation (2) as,

2 = sqrt(x+2)

square this equation,

4 = x+2

Then x = 2.

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