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Problems
Contests
National and Regional Contests
Morocco Contests
Morocco National Olympiad
2011 Morocco National Olympiad
3
Max and min
Max and min
Source: Morocco 2011
April 24, 2011
inequalities unsolved
inequalities
Problem Statement
Let
a
a
a
and
b
b
b
be two real numbers and let
M
(
a
,
b
)
=
max
{
3
a
2
+
2
b
;
3
b
2
+
2
a
}
M(a,b)=\max\left \{ 3a^{2}+2b; 3b^{2}+2a\right \}
M
(
a
,
b
)
=
max
{
3
a
2
+
2
b
;
3
b
2
+
2
a
}
. Find the values of
a
a
a
and
b
b
b
for which
M
(
a
,
b
)
M(a,b)
M
(
a
,
b
)
is minimal.
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