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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2009 Junior Balkan Team Selection Tests - Moldova
2
\frac{a^2+b^2}{a^4+b^4}+\frac{b^2+c^2}{b^4+c^4}+\frac{c^2+a^2}{c^4+a^4}
\frac{a^2+b^2}{a^4+b^4}+\frac{b^2+c^2}{b^4+c^4}+\frac{c^2+a^2}{c^4+a^4}
Source: Moldova JTST 2009
May 10, 2023
inequalities
Problem Statement
Real positive numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
a
b
c
=
1
abc=1
ab
c
=
1
. Prove the inequality
a
2
+
b
2
a
4
+
b
4
+
b
2
+
c
2
b
4
+
c
4
+
c
2
+
a
2
c
4
+
a
4
≤
a
+
b
+
c
.
\frac{a^2+b^2}{a^4+b^4}+\frac{b^2+c^2}{b^4+c^4}+\frac{c^2+a^2}{c^4+a^4}\leq a+b+c.
a
4
+
b
4
a
2
+
b
2
+
b
4
+
c
4
b
2
+
c
2
+
c
4
+
a
4
c
2
+
a
2
≤
a
+
b
+
c
.
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