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National and Regional Contests
South Africa Contests
South Africa National Olympiad
2008 South africa National Olympiad
3
3
Part of
2008 South africa National Olympiad
Problems
(1)
Product (a+b) > 8 Product (a+b-c)
Source: South African MO 2008 Q3
5/27/2012
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers. Prove that
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
8
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
(a+b)(b+c)(c+a)\ge 8(a+b-c)(b+c-a)(c+a-b)
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
8
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
and determine when equality occurs.
inequalities
inequalities unsolved