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2007 JBMO Shortlist
2
Adding 1
Adding 1
Source: JBMO Shortlist 2007
May 12, 2016
inequalities
algebra
Problem Statement
A2
\boxed{\text{A2}}
A2
Prove that for all Positive reals
a
,
b
,
c
a,b,c
a
,
b
,
c
a
2
−
b
c
2
a
2
+
b
c
+
b
2
−
c
a
2
b
2
+
c
a
+
c
2
−
a
b
2
c
2
+
a
b
≤
0
\frac{a^2-bc}{2a^2+bc}+\frac{b^2-ca}{2b^2+ca}+\frac{c^2-ab}{2c^2+ab}\leq 0
2
a
2
+
b
c
a
2
−
b
c
+
2
b
2
+
c
a
b
2
−
c
a
+
2
c
2
+
ab
c
2
−
ab
≤
0
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