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Putnam
1953 Putnam
A3
1953 Putnam A3
1953 Putnam A3
Source: 1953 Putnam A3
August 20, 2021
Putnam
inequalities
Problem Statement
a
,
b
,
c
a, b, c
a
,
b
,
c
are real, and the sum of any two is greater than the third. Show that
2
(
a
+
b
+
c
)
(
a
2
+
b
2
+
c
2
)
3
>
a
3
+
b
3
+
c
3
+
a
b
c
\frac{2(a + b + c)(a^2 + b^2 + c^2)}{3} > a^3 + b^3 + c^3 + abc
3
2
(
a
+
b
+
c
)
(
a
2
+
b
2
+
c
2
)
>
a
3
+
b
3
+
c
3
+
ab
c
.
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