8. When $a$ and $b$ are two distinct 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
A. Definitely 甲
B. Definitely 乙
C. Definitely 丙
D. Generally not certain, and depends on the values of $a$ and $b$
By the Cauchy inequality $\left(a+\frac{1}{a}\right)\left(b+\frac{1}{b}\right) \geqslant\left(\sqrt{a b}+\frac{1}{\sqrt{a b}}\right)^{2}$, we only need to compare A and C. When $a=2, b=1$, A $=\frac{5}{2} \cdot 2=5$, C $=\left(\frac{3}{2}+\frac{2}{3}\right)^{2}=\frac{169}{36}$, A $>$ B; when $a=5, b=1$, A $=\frac{26}{5} \cdot 2=\frac{52}{5}$, C $=\left(3+\frac{1}{3}\right)^{2}=\frac{100}{9}$, A $<$ B. Therefore, the answer is $D$.