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2014 Estonia Team Selection Test
2
sum a^2/(b^3 + c^4 + 1) > 1/5
sum a^2/(b^3 + c^4 + 1) > 1/5
Source: Estonia IMO TST 2014 p2
April 5, 2020
inequalities
algebra
Problem Statement
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive real numbers for which
a
+
b
+
c
=
1
a + b + c = 1
a
+
b
+
c
=
1
. Prove that
a
2
b
3
+
c
4
+
1
+
b
2
c
3
+
a
4
+
1
+
c
2
a
3
+
b
4
+
1
>
1
5
\frac{a^2}{b^3 + c^4 + 1}+\frac{b^2}{c^3 + a^4 + 1}+\frac{c^2}{a^3 + b^4 + 1} > \frac{1}{5}
b
3
+
c
4
+
1
a
2
+
c
3
+
a
4
+
1
b
2
+
a
3
+
b
4
+
1
c
2
>
5
1
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