2-110 Let the sequence of positive real numbers $x_{0}, x_{1}, \cdots, x_{1995}$ satisfy the following two conditions:
(1) $x_{0}=x_{1995}$;
(2) $x_{i-1}+\frac{2}{x_{i-1}}=2 x_{i}+\frac{1}{x_{i}}, i=1,2, \cdots, 1995$.

Find the maximum value of $x_{0}$ for all sequences satisfying the above conditions.
【Solution】 From condition (2), we know
$$\begin{array}{l}
x_{i}^{2}-\left(\frac{x_{i-1}}{2}+\frac{1}{x_{i-1}}\right) x_{i}+\frac{1}{2}=0, \\
\left(x_{i}-\frac{x_{i-1}}{2}\right)\left(x_{i}-\frac{1}{x_{i-1}}\right)=0, \\
x_{i}=\frac{x_{i-1}}{2} \text { or } x_{i}=\frac{1}{x_{i-1}} .
\end{array}$$

The transformation that changes $x_{i-1}$ to $x_{i}=\frac{x_{i-1}}{2}$ is called the first type of transformation, and the transformation that changes $x_{i-1}$ to $x_{i}=\frac{1}{x_{i-1}}$ is called the second type of transformation. If starting from $x_{0}$, a total of $k-t$ first type transformations and $t$ second type transformations are experienced to get $x_{k}$. Note that if two first type transformations are separated by an odd number of second type transformations, the effects of these two first type transformations cancel each other out. Therefore,
$$x_{k}=2^{s} x_{0}^{(-1)^{t}}$$

where $S \equiv k-t(\bmod 2)$.
When $k=1995$, if $t$ is even, then
$$\left\{\begin{array}{l}
x_{0}=x_{1995}=2^{s} \cdot x_{0} \\
S \equiv 1995(\bmod 2)
\end{array}\right.$$

which means
$$\left\{\begin{array}{l}2^{s}=1, \\ S \text { is odd. }\end{array}\right.$$
This is clearly impossible. Therefore, $t$ is odd. Thus, we have
$$\begin{array}{l}
x_{0}=2^{s} \cdot \frac{1}{x_{0}} \\
x_{0}=2^{\frac{s}{2}}
\end{array}$$

Since $S$ is even, we have
$$\begin{array}{l}
S \leqslant|s| \leqslant 1994 \\
x_{0} \leqslant 2^{997}
\end{array}$$

On the other hand, we have the sequence $x_{0}, x_{1}, \cdots, x_{1995}$, where $x_{0}=2^{997}, x_{i}=$
$$\begin{array}{l}
\frac{x_{i-1}}{2}(i=1,2, \cdots, 1994) \\
\quad x_{1995}=\frac{1}{x_{1994}}=\frac{1}{\frac{2^{997}}{2^{1994}}}=2^{997}=x_{0}
\end{array}$$

In summary, the maximum value of $x_{0}$ is $2^{997}$.