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Canada National Olympiad
1995 Canada National Olympiad
2
Exponential Inequality
Exponential Inequality
Source: Canadian Mathematical Olympiad - 1995 - Problem 2.
May 9, 2011
inequalities
logarithms
inequalities proposed
Problem Statement
Let
{
a
,
b
,
c
}
∈
R
+
\{a,b,c\}\in \mathbb{R}^{+}
{
a
,
b
,
c
}
∈
R
+
. Prove that
a
a
b
b
c
c
≥
(
a
b
c
)
a
+
b
+
c
3
a^a b^b c^c \ge (abc)^{\frac{a+b+c}{3}}
a
a
b
b
c
c
≥
(
ab
c
)
3
a
+
b
+
c
.
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