Question 49
Does there exist a positive real number $C$ such that the inequality
$$
x_1x_2 + x_1x_3 + x_1x_4 + x_2x_3 + x_2x_4 + x_3x_4 \le C(x_1x_2 + x_2x_3 + x_3x_4 + x_4x_1)
$$
holds for arbitrary positive real numbers $x_1, x_2, x_3, x_4$?
$$
x_1x_2 + x_1x_3 + x_1x_4 + x_2x_3 + x_2x_4 + x_3x_4 \le C(x_1x_2 + x_2x_3 + x_3x_4 + x_4x_1)
$$
holds for arbitrary positive real numbers $x_1, x_2, x_3, x_4$?