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Azerbaijan Contests
Azerbaijan Junior National Olympiad
2015 Azerbaijan National Olympiad
1
Azerbaijan NMO 2015
Azerbaijan NMO 2015
Source: Azerbaijan NMO 2015
October 21, 2015
inequalities
algebra
Problem Statement
Let
a
,
b
a,b
a
,
b
and
c
c
c
be positive reals such that
a
b
c
=
1
8
abc=\frac{1}{8}
ab
c
=
8
1
.Then prove that
a
2
+
b
2
+
c
2
+
a
2
b
2
+
a
2
c
2
+
b
2
c
2
≥
15
16
a^2+b^2+c^2+a^2b^2+a^2c^2+b^2c^2\ge\frac{15}{16}
a
2
+
b
2
+
c
2
+
a
2
b
2
+
a
2
c
2
+
b
2
c
2
≥
16
15
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