USAMO
Guide
Home
Contests
Problemset
Standings
Announcements
…
Back to Problems
Prev
Next
1900
Constrained Minimum
Editorial
algebra
optimization
symmetric expressions
AM-GM
inequalities
Given real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
with
a
b
c
=
4
abc = 4
ab
c
=
4
and
a
+
b
+
c
=
5
a + b + c = 5
a
+
b
+
c
=
5
, find the minimum value of
(
a
+
b
+
c
)
(
a
2
b
2
+
b
2
c
2
+
a
2
c
2
)
.
(a+b+c)(a^2b^2 + b^2c^2 + a^2c^2).
(
a
+
b
+
c
)
(
a
2
b
2
+
b
2
c
2
+
a
2
c
2
)
.
Round your answer to the nearest integer.
Sign in to submit your answer
Sign In
