8. When $a, b$ are two unequal positive numbers, among the following three algebraic expressions:

甲: $\left(a+\frac{1}{a}\right)\left(b+\frac{1}{b}\right)$,
乙: $\left(\sqrt{a b}+\frac{1}{\sqrt{a b}}\right)^{2}$,

丙: $\left(\frac{a+b}{2}+\frac{2}{a+b}\right)^{2}$.
the one with the largest value is
Answer ( )
(A) must be 甲
(B) must be 乙
(C) must be 丙
(D) generally is not certain, and depends on the values of $a, b$
Answer ( )
(D)
8.【Analysis and Solution】Let $a=\left(a+\frac{1}{a}\right)\left(b+\frac{1}{b}\right)=a b+\frac{1}{a b}+\frac{b}{a}+\frac{a}{b}$
$$
\begin{array}{l}
>a b+\frac{1}{a b}+2 \\
=\left(\sqrt{a b}+\frac{1}{\sqrt{a b}}\right)^{2}=\text { Yi. }
\end{array}
$$
$\therefore$ Ji $>$ Yi. Therefore, the largest one cannot be Yi, eliminating (B). We only need to compare the sizes of Ji and Bing. Taking special values $a=1, b=2$ we get
$$
\text { Ji }=(1+1)\left(2+\frac{1}{2}\right)=5 \text {, Bing }=\left(\frac{3}{2}+\frac{2}{3}\right)^{2}=4 \frac{25}{36} \text {. }
$$
$\therefore$ Ji $>$ Bing, so Bing will not be the largest, eliminating $(\mathrm{C})$.
Let $a=1, b=5$,
$$
\text { Ji }=(1+1)\left(5+\frac{1}{5}\right)=10 \frac{2}{5} \text {, Bing }=\left(\frac{6}{2}+\frac{2}{6}\right)^{2}=11 \frac{1}{9} \text {. }
$$

So in this case Ji < Bing, so Ji will not be the largest value, eliminating (A).