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Switzerland Contests
Switzerland - Final Round
2013 Switzerland - Final Round
8
8
Part of
2013 Switzerland - Final Round
Problems
(1)
sum a^2 (a - b)(a + b) >0
Source: Switzerland - 2013 Swiss MO Final Round p8
1/14/2023
Let
a
,
b
,
c
>
0
a, b, c > 0
a
,
b
,
c
>
0
be real numbers. Show the following inequality:
a
2
⋅
a
−
b
a
+
b
+
b
2
⋅
b
−
c
b
+
c
+
c
2
⋅
c
−
a
c
+
a
≥
0.
a^2 \cdot \frac{a - b}{a + b}+ b^2\cdot \frac{b - c}{b + c}+ c^2\cdot \frac{c - a}{c + a} \ge 0 .
a
2
⋅
a
+
b
a
−
b
+
b
2
⋅
b
+
c
b
−
c
+
c
2
⋅
c
+
a
c
−
a
≥
0.
When does equality holds?
algebra
inequalities