is this the right question?
i can prove
a/b+b/c+c/a≥3^(1/3){(a2+b2+c2)/(ab+bc+ca)}^(2/3)
$If $\mathbf{a,b,c\in \mathbb{R^{+}}}$.Then prove that \\\\ $\mathbf{\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\geq 3.\left(\frac{a^2+b^2+c^2}{ab+bc+ca}\right)^{\frac{2}{3}}}$\\\\
is this the right question?
i can prove
a/b+b/c+c/a≥3^(1/3){(a2+b2+c2)/(ab+bc+ca)}^(2/3)