MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
USAMO
1991 USAMO
4
4
Part of
1991 USAMO
Problems
(1)
Bernoulli's inequality
Source:
10/11/2005
Let
a
=
m
m
+
1
+
n
n
+
1
m
m
+
n
n
a = \frac{m^{m+1} + n^{n+1}}{m^m + n^n}
a
=
m
m
+
n
n
m
m
+
1
+
n
n
+
1
, where
m
m
m
and
n
n
n
are positive integers. Prove that
a
m
+
a
n
≥
m
m
+
n
n
a^m + a^n \geq m^m + n^n
a
m
+
a
n
≥
m
m
+
n
n
.
inequalities
AMC
USA(J)MO
USAMO
inequalities unsolved
1991