IMO Shortlist 1968 problem 12
Dodao/la:
arhiva2. travnja 2012. If
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
and
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
are arbitrary positive real numbers and
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
an integer, prove that
%V0
If $a$ and $b$ are arbitrary positive real numbers and $m$ an integer, prove that
$$\Bigr( 1+\frac ab \Bigl)^m +\Bigr( 1+\frac ba \Bigl)^m \geq 2^{m+1}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1968