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Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2005 Switzerland - Final Round
6
6
Part of
2005 Switzerland - Final Round
Problems
(1)
sum (1+a)/(1+a+ab) where abc=1
Source: Switzerland - 2005 Swiss MO Final Round p6
12/26/2022
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers with
a
b
c
=
1
abc = 1
ab
c
=
1
. Find all possible values of the expression
1
+
a
1
+
a
+
a
b
+
1
+
b
1
+
b
+
b
c
+
1
+
c
1
+
c
+
c
a
\frac{1 + a}{1 + a + ab}+\frac{1 + b}{1 + b + bc}+\frac{1 + c}{1 + c + ca}
1
+
a
+
ab
1
+
a
+
1
+
b
+
b
c
1
+
b
+
1
+
c
+
c
a
1
+
c
can take.
algebra
Sum