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4
Power sum inequalities
Power sum inequalities
Source: 2013 SDMO Middle School Problem 4
August 25, 2016
inequalities
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
, and
d
d
d
be positive real numbers such that
a
+
b
=
c
+
d
a+b=c+d
a
+
b
=
c
+
d
and
a
2
+
b
2
>
c
2
+
d
2
a^2+b^2>c^2+d^2
a
2
+
b
2
>
c
2
+
d
2
. Prove that
a
3
+
b
3
>
c
3
+
d
3
a^3+b^3>c^3+d^3
a
3
+
b
3
>
c
3
+
d
3
.
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