IMO Shortlist 1966 problem 46
Dodao/la:
arhiva2. travnja 2012. Let
![a,b,c](/media/m/3/6/4/36454fdb50fc50f021324b33a6b513e3.png)
be reals and
![f(a, b, c) = \left| \frac{ |b-a|}{|ab|} +\frac{b+a}{ab} -\frac 2c \right| +\frac{ |b-a|}{|ab|} +\frac{b+a}{ab} +\frac 2c](/media/m/d/2/3/d2307c9775d35f3024f6f060a784ad6f.png)
Prove that
%V0
Let $a,b,c$ be reals and
$$f(a, b, c) = \left| \frac{ |b-a|}{|ab|} +\frac{b+a}{ab} -\frac 2c \right| +\frac{ |b-a|}{|ab|} +\frac{b+a}{ab} +\frac 2c$$
Prove that $f(a, b, c) = 4 \max \{\frac 1a, \frac 1b,\frac 1c \}.$
Izvor: Međunarodna matematička olimpijada, shortlist 1966