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Bulgaria JBMO Team Selection Test
2018 Bulgaria JBMO TST
2
(a^2+b^2)/(2a^5b^5) + (81a^2b^2)/4 + 9ab \geq 81
(a^2+b^2)/(2a^5b^5) + (81a^2b^2)/4 + 9ab \geq 81
Source: Bulgaria JBMO TST 2018, Day 1, Problem 2
June 25, 2018
inequalities
Problem Statement
For all positive reals
a
a
a
and
b
b
b
, show that
a
2
+
b
2
2
a
5
b
5
+
81
a
2
b
2
4
+
9
a
b
>
18.
\frac{a^2+b^2}{2a^5b^5} + \frac{81a^2b^2}{4} + 9ab > 18.
2
a
5
b
5
a
2
+
b
2
+
4
81
a
2
b
2
+
9
ab
>
18.
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