We have:\(a+\dfrac{1}{b}+b+\dfrac{1}{c}+c+\dfrac{1}{a}< 6\)

But \(a+\dfrac{1}{a}+b+\dfrac{1}{b}+c+\dfrac{1}{c}\ge2\sqrt{a.\dfrac{1}{a}}+2\sqrt{b.\dfrac{1}{b}}+2\sqrt{c.\dfrac{1}{c}}=2+2+2=6\)

So there are no a,b,c>0 satisfys