(2) If the equation $x^{2}+(a+2) x-2 a$ $+1=0$ has two distinct real roots with respect to $x$, find the range of values for its larger root.
(Wu Weizhao)
(2) The larger root of $f_{a}(x)=0$ is
$$
\begin{aligned}
x & =\frac{-(a+2)+\sqrt{(a+2)^{2}-4(1-2 a)}}{2} \\
& =\frac{-(a+2)+\sqrt{a^{2}+12 a}}{2} \\
& =\frac{-(a+2)+\sqrt{(a+6)^{2}-36}}{2} .
\end{aligned}
$$

Let $a+6=2 k$. Then
$$
x=\frac{-(2 k-4)+\sqrt{4 k^{2}-36}}{2}=\sqrt{k^{2}-9}-k+2 \text {. }
$$

By $\Delta>0$, we get $k>3$ or $k>5$;
When $k>3$, $x=2-\frac{9}{\sqrt{k^{2}-9}+k}$, we can get $-1<x<2$.
In summary, the range of the larger root $x$ of the equation is $(-1,2) \cup(5,+\infty)$.