MathDB
SRMC 2015 inequality P1

Source:

April 3, 2015
inequalitiesalgebra

Problem Statement

Given positive real numbers a,b,c,da,b,c,d such that
\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}=6   \text{and}   \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}=36.
Prove the inequality
a2+b2+c2+d2>ab+ac+ad+bc+bd+cd.{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+{{d}^{2}}>ab+ac+ad+bc+bd+cd.
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