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Bosnia and Herzegovina JBMO TST 2009 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2009

September 17, 2018
algebraInequalitypositive real

Problem Statement

Let aa , bb, cc and dd be positive real numbers such that a+b+c+d=8a+b+c+d=8. Prove that 1a+1b+4c+16d≥8\frac{1}{a}+\frac{1}{b}+\frac{4}{c}+\frac{16}{d}\geq8
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