MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2015 Harvard-MIT Mathematics Tournament
5
2015 Algebra #5: Maximum of Minimum of Expression
2015 Algebra #5: Maximum of Minimum of Expression
Source:
March 28, 2015
algebra
inequalities
maximization
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
a
+
b
+
c
=
10
a+b+c=10
a
+
b
+
c
=
10
and
a
b
+
b
c
+
c
a
=
25
ab+bc+ca=25
ab
+
b
c
+
c
a
=
25
. Let
m
=
min
{
a
b
,
b
c
,
c
a
}
m=\min\{ab,bc,ca\}
m
=
min
{
ab
,
b
c
,
c
a
}
. Find the largest possible value of
m
m
m
.
Back to Problems
View on AoPS