Question 8
II 2 (NET 3), IMO5
If $a,b,c,d$ are arbitrary positive real numbers, find all possible values of
$$S=\frac a{a+b+d}+\frac b{a+b+c}+\frac c{b+c+d}+\frac d{a+c+d}.$$
If $a,b,c,d$ are arbitrary positive real numbers, find all possible values of
$$S=\frac a{a+b+d}+\frac b{a+b+c}+\frac c{b+c+d}+\frac d{a+c+d}.$$