MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2012 Junior Balkan Team Selection Tests - Moldova
2
Simple Inequality
Simple Inequality
Source: Moldova JBMO TST 2012
August 9, 2012
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers, prove the inequality:
(
a
+
b
+
c
)
2
+
a
b
+
b
c
+
a
c
≥
6
a
b
c
(
a
+
b
+
c
)
(a+b+c)^2+ab+bc+ac\geq 6\sqrt{abc(a+b+c)}
(
a
+
b
+
c
)
2
+
ab
+
b
c
+
a
c
≥
6
ab
c
(
a
+
b
+
c
)
Back to Problems
View on AoPS