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Baltic Way
2003 Baltic Way
4
a,b,c inequality [Baltic Way 2003]
a,b,c inequality [Baltic Way 2003]
Source:
November 5, 2010
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers. Prove that
2
a
a
2
+
b
c
+
2
b
b
2
+
c
a
+
2
c
c
2
+
a
b
≤
a
b
c
+
b
c
a
+
c
a
b
\frac{2a}{a^{2}+bc}+\frac{2b}{b^{2}+ca}+\frac{2c}{c^{2}+ab}\leq\frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab}
a
2
+
b
c
2
a
+
b
2
+
c
a
2
b
+
c
2
+
ab
2
c
≤
b
c
a
+
c
a
b
+
ab
c
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