To solve the equation , we can start by simplifying it. Since the expression inside the square roots is recursively defined, we can make a substitution by letting:

Thus, the equation simplifies to:

Now, squaring both sides gives us:

Rearranging this, we have:

This is a quadratic equation in terms of . We can now use the quadratic formula:

where :

Now, since must be non-negative (as it represents a square root), we take the positive solution:

Finally, substituting back into the equation , we have:

To solve for , we multiply through by 2:

Subtracting 1 from both sides:

Now square both sides:

Expanding the left side:

Combining like terms gives:

Factoring out :

Thus, the solutions are or .

Finally, we can check against the original expression, and both values satisfy it. Therefore, the solutions to the original equation are and .