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National and Regional Contests
Kazakhstan Contests
Kazakhstan National Olympiad
2021 Kazakhstan National Olympiad
1
1
Part of
2021 Kazakhstan National Olympiad
Problems
(1)
İnequality
Source: Kazakhstan JMO 2021, Problem 1.
4/28/2021
Given
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
such that
a
+
b
+
c
+
1
a
b
c
=
19
2
a+b+c+\frac{1}{abc}=\frac{19}{2}
a
+
b
+
c
+
ab
c
1
=
2
19
What is the greatest value for
a
a
a
?
Kazakhstan
inequalities proposed
inequalities