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National and Regional Contests
Bulgaria Contests
Bulgaria JBMO Team Selection Test
2016 Bulgaria JBMO TST
2
Inequality
Inequality
Source: Bulgaria JTST 2016 P2 day 1
August 27, 2019
Inequality proposed
inequalities
Problem Statement
a, b, c are positive real numbers and a+b+c=k. Find the minimum value of
b
2
/
(
k
a
+
b
c
)
1
/
2
+
c
2
/
(
k
b
+
a
c
)
1
/
2
+
a
2
/
(
k
c
+
a
b
)
1
/
2
b^2/(ka+bc)^1/2+c^2/(kb+ac)^1/2+a^2/(kc+ab)^1/2
b
2
/
(
ka
+
b
c
)
1
/2
+
c
2
/
(
kb
+
a
c
)
1
/2
+
a
2
/
(
k
c
+
ab
)
1
/2
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