Question 20
Find the greatest constant $M$ such that
$$
a^2 + b^2 + c^2 + 3abc \geq M(ab + bc + ca)
$$
for all nonnegative real numbers $a, b, c$ satisfying $a + b + c = 4$.
$$
a^2 + b^2 + c^2 + 3abc \geq M(ab + bc + ca)
$$
for all nonnegative real numbers $a, b, c$ satisfying $a + b + c = 4$.