Question 34
Find all the real numbers $k$ such that
$$
\sqrt{3(a^2 + b^2 + c^2)} \leq a + b + c + k\sqrt{a^2 + b^2 + c^2 - ab - bc - ca},
$$
for every positive real numbers $a$, $b$, $c$.
$$
\sqrt{3(a^2 + b^2 + c^2)} \leq a + b + c + k\sqrt{a^2 + b^2 + c^2 - ab - bc - ca},
$$
for every positive real numbers $a$, $b$, $c$.