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Kyiv City MO
2021 Kyiv City MO
2021 Kyiv City MO Round 1
11.4
11.4
Part of
2021 Kyiv City MO Round 1
Problems
(1)
Another amazing inequality
Source: Kyiv City MO 2021 Round 1, Problem 11.4
12/21/2023
For positive real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
with sum
3
2
\frac{3}{2}
2
3
, find the smallest possible value of the following expression:
a
3
b
c
+
b
3
c
a
+
c
3
a
b
+
1
a
b
c
\frac{a^3}{bc} + \frac{b^3}{ca} + \frac{c^3}{ab} + \frac{1}{abc}
b
c
a
3
+
c
a
b
3
+
ab
c
3
+
ab
c
1
Proposed by Serhii Torba
inequalities
algebra
inequalities proposed