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National and Regional Contests
Vietnam Contests
Pre - Vietnam Mathematical Olympiad
2012 Pre - Vietnam Mathematical Olympiad
1
Simple Inequality
Simple Inequality
Source: Pre-VMO 2012 - Round 2 - Problem 1
December 25, 2011
inequalities
logarithms
calculus
derivative
inequalities proposed
Problem Statement
For
a
,
b
,
c
>
0
:
a
b
c
=
1
a,b,c>0: \; abc=1
a
,
b
,
c
>
0
:
ab
c
=
1
prove that
a
3
+
b
3
+
c
3
+
6
≥
(
a
+
b
+
c
)
2
a^3+b^3+c^3+6 \ge (a+b+c)^2
a
3
+
b
3
+
c
3
+
6
≥
(
a
+
b
+
c
)
2
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