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Saint Petersburg Mathematical Olympiad
2010 Saint Petersburg Mathematical Olympiad
6
Inequality
Inequality
Source: St Petersburg Olympiad 2010, Grade 9, P6
September 14, 2017
algebra
inequalities
Problem Statement
For positive is true
3
a
b
c
≥
a
+
b
+
c
\frac{3}{abc} \geq a+b+c
ab
c
3
≥
a
+
b
+
c
Prove
1
a
+
1
b
+
1
c
≥
a
+
b
+
c
\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \geq a+b+c
a
1
+
b
1
+
c
1
≥
a
+
b
+
c
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