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1978 IMO Longlists
45
Proving an inequality involving powers
Proving an inequality involving powers
Source:
October 31, 2010
inequalities
induction
inequalities unsolved
Problem Statement
If
r
>
s
>
0
r > s >0
r
>
s
>
0
and
a
>
b
>
c
a > b > c
a
>
b
>
c
, prove that
a
r
b
s
+
b
r
c
s
+
c
r
a
s
≥
a
s
b
r
+
b
s
c
r
+
c
s
a
r
.
a^rb^s + b^rc^s + c^ra^s \ge a^sb^r + b^sc^r + c^sa^r.
a
r
b
s
+
b
r
c
s
+
c
r
a
s
≥
a
s
b
r
+
b
s
c
r
+
c
s
a
r
.
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