2. (7p) Consider the positive real numbers $a, b, c, d$, such that $a b c d=1$. Calculate

$$
E=\frac{7+a}{1+a+a b+a b c}+\frac{7+b}{1+b+b c+b c d}+\frac{7+c}{1+c+c d+c d a}+\frac{7+d}{1+d+d a+d a b}
$$

GM11/2015
2. By amplifying the second ratio by $a$, the third by $a b$, and the fourth by $a b c$, we obtain:

$E=\frac{7+a}{1+a+a b+a b c}+\frac{(7+b) a}{a+a b+a b c+1}+\frac{(7+c) a b}{a b+a b c+1+a}+\frac{(7+d) a b c}{a b c+1+a+a b}$ $\qquad$
(4p)

$E=8$

(3p)