[68] - Algebraic Inequalities from and for Math Contests

Έστω $a, b, c>0$ και $a^2+b^2+c^2=abc$. Να αποδειχθεί ότι $$\displaystyle 2(a+b+c)+\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab} \le abc.$$