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National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2015 Switzerland - Final Round
7
7
Part of
2015 Switzerland - Final Round
Problems
(1)
sum a^2/(b + c) =? if sum a/(b + c)=1
Source: Switzerland - 2015 Swiss MO Final Round p7
1/14/2023
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be real numbers such that:
a
b
+
c
+
b
c
+
a
+
c
a
+
b
=
1
\frac{a}{b + c}+\frac{b}{c + a}+\frac{c}{a + b}= 1
b
+
c
a
+
c
+
a
b
+
a
+
b
c
=
1
Determine all values which the following expression can take :
a
2
b
+
c
+
b
2
c
+
a
+
c
2
a
+
b
.
\frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b}.
b
+
c
a
2
+
c
+
a
b
2
+
a
+
b
c
2
.
algebra
Sum