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2002 Canada National Olympiad
3
Really classical inequatily from canada
Really classical inequatily from canada
Source: Canada 2002
March 5, 2006
inequalities
Canada
AM-GM
am-gm inequality
algebra
Problem Statement
Prove that for all positive real numbers
a
a
a
,
b
b
b
, and
c
c
c
,
a
3
b
c
+
b
3
c
a
+
c
3
a
b
≥
a
+
b
+
c
\frac{a^3}{bc} + \frac{b^3}{ca} + \frac{c^3}{ab} \geq a+b+c
b
c
a
3
+
c
a
b
3
+
ab
c
3
≥
a
+
b
+
c
and determine when equality occurs.
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