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Vietnam Contests
Vietnam Team Selection Test
1996 Vietnam Team Selection Test
3
(a+b)^4+(b+c)^4+(c+a)^4 - product
(a+b)^4+(b+c)^4+(c+a)^4 - product
Source: Vietnam TST 1996 for the 37th IMO, problem 3
June 26, 2005
inequalities
inequalities unsolved
Problem Statement
Find the minimum value of the expression:
f
(
a
,
b
,
c
)
=
(
a
+
b
)
4
+
(
b
+
c
)
4
+
(
c
+
a
)
4
−
4
7
⋅
(
a
4
+
b
4
+
c
4
)
.
f(a,b,c)= (a+b)^4+(b+c)^4+(c+a)^4 - \frac{4}{7} \cdot (a^4+b^4+c^4).
f
(
a
,
b
,
c
)
=
(
a
+
b
)
4
+
(
b
+
c
)
4
+
(
c
+
a
)
4
−
7
4
⋅
(
a
4
+
b
4
+
c
4
)
.
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