MRF2017 wrote: Prove that there is no positive real numbers $a,b,c,d$ such that both of the following equations hold.$$\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}=6 , \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}=32$$. SRMC 2015 Given positive real numbers $a,b,c,d$ such that $ \frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}=6 \quad \text{and} \quad \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}=36.$Prove the inequality $${{a}^{2}}+{{b}^{2}}+{{c}^{2}}+{{d}^{2}}>ab+ac+ad+bc+bd+cd.$$