Question 89
Find all real numbers $r$ such that the inequality
$$
r(ab + bc + ca) + (3 - r) \left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) \ge 9
$$
holds true for arbitrary positive numbers $a, b$ and $c$.
$$
r(ab + bc + ca) + (3 - r) \left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right) \ge 9
$$
holds true for arbitrary positive numbers $a, b$ and $c$.