2. Let $x_{n} y$ satisfy $x_{1}=x_{2}=1, x_{n+1}=\frac{x_{n} \cdot x_{n}-1}{x_{n}+x_{n-1}}(n \geqslant 2)$, then $x_{10}=(\quad)$.
A. $\frac{1}{21}$
B. $\frac{1}{34}$
C. $\frac{1}{55}$
D. $\frac{1}{89}$
$2, C$
From $x_{n+1}=\frac{x_{n} \cdot x_{n-1}}{x_{n}+x_{n-1}} \Rightarrow \frac{1}{x_{n+\mathrm{i}}}=\frac{1}{x_{n}}+\frac{1}{x_{n-1}} \Rightarrow \frac{1}{x_{0}}$
$$
=55 \Rightarrow x_{10}=\frac{1}{55} \text {. }
$$