MathDB

1 (original)

Part of 2015 Silk Road

Problems(1)

SRMC 2015 inequality P1

Source:

4/3/2015
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.
inequalitiesalgebra