Cho $a,\,b,\,c>0$ thỏa $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=3$. Chứng minh rằng:$$\sqrt{\dfrac{9}{2}+\dfrac{3}{4}\left(\dfrac{a+b}{c}+\dfrac{b+c}{a}+\dfrac{c+a}{b}
\right)}\geq \sqrt{\dfrac{a+b}{c+ab}}+\sqrt{\dfrac{b+c}{a+bc}}+
\sqrt{\dfrac{c+a}{b+ca}}$$