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National and Regional Contests
Lithuania Contests
Lithuania National Olympiad
2010 Lithuania National Olympiad
1
the range of a+b
the range of a+b
Source: Lithuania NMO 2010
March 11, 2012
inequalities proposed
inequalities
Problem Statement
a
,
b
a,b
a
,
b
are real numbers such that:
a
3
+
b
3
=
8
ā
6
a
b
.
a^3+b^3=8-6ab.
a
3
+
b
3
=
8
ā
6
ab
.
Find the maximal and minimal value of
a
+
b
a+b
a
+
b
.
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