$77 a$ is the arithmetic mean of the real numbers $2 x, 2 y$, $\sqrt{|a|}$ is the geometric mean of $x, y$, then the range of the real number $a$ is
A. $(0,4]$
B. $(-\infty, 0) \cup[4,+\infty)$
C. $[-4,0) \cup(0,4]$
D. $(-\infty,-4] \cup(4,+\infty)$
77 D. According to the problem, we have
$$
\left\{\begin{array}{l}
x+y=a, \\
x y=|a|
\end{array}\right.
$$

Therefore, $x, y$ are the roots of the equation
$$
z^{2}-a z+|a|=0
$$

Thus, we have
$$
\left\{\begin{array}{l}
a>0 \\
a^{2}-4 a \geqslant 0,
\end{array}\right.
$$

or
$$
\left\{\begin{array}{l}
a<0, \\
a^{2}+4 a \geqslant 0,
\end{array}\right.
$$

Solving this, we get $a \leqslant-4$ or $a \geqslant 4$.