IMO Shortlist 1971 problem 17


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Dodao/la: arhiva
April 2, 2012
1971 alg nejednakost shortlist
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Prove the inequality
\frac{a_1+ a_3}{a_1 + a_2} + \frac{a_2 + a_4}{a_2 + a_3} + \frac{a_3 + a_1}{a_3 + a_4} + \frac{a_4 + a_2}{a_4 + a_1} \geq 4,
where a_i > 0, i = 1, 2, 3, 4.
Source: Međunarodna matematička olimpijada, shortlist 1971