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IMO Shortlist
1968 IMO Shortlist
12
12
Part of
1968 IMO Shortlist
Problems
(1)
Inequality holds for any integer m and positive reals a, b
Source:
9/23/2010
If
a
a
a
and
b
b
b
are arbitrary positive real numbers and
m
m
m
an integer, prove that
(
1
+
a
b
)
m
+
(
1
+
b
a
)
m
≥
2
m
+
1
.
\Bigr( 1+\frac ab \Bigl)^m +\Bigr( 1+\frac ba \Bigl)^m \geq 2^{m+1}.
(
1
+
b
a
)
m
+
(
1
+
a
b
)
m
≥
2
m
+
1
.
induction
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Inequality
algebra
2-variable inequality
IMO Shortlist
inequalities