Question 3: Given the set $A=\{x \mid 1 \leq x \leq 4\}, B=\left\{x \mid x^{2}-2 a x+a+2=0\right\} (a \in R)$, and $B \subseteq$
$A$, try to find the range of values for $a$.

保留了原文的换行和格式，如上所示。
Question 3, Answer: When $\Delta=(2 a)^{2}-4(a+2)<0 \Leftrightarrow a \in(-1,2)$, $B=\emptyset$, which clearly satisfies the condition. When $B \neq \varnothing$, i.e., $a \in(-\infty,-1) \cup[2,+\infty)$, let $f(x)=x^{2}-2 a x+a+2$, then $a$ satisfies the condition if and only if
$$
\left\{\begin{array} { c } 
{ 1 \leq - \frac { - 2 a } { 2 } \leq 4 } \\
{ f ( 1 ) \geq 0 } \\
{ f ( 4 ) \geq 0 }
\end{array} \Leftrightarrow \left\{\begin{array}{c}
1 \leq a \leq 4 \\
a \leq 3 \\
a \leq \frac{18}{7}
\end{array}\right.\right.
$$

In summary, the range of values for $a$ that satisfy the condition is $\left(-1, \frac{18}{7}\right)$.