Question 141
Find the least value of $k \gt 0$ such that
$$
|x - ky| + |y - kz| + |z - kx| \geq 7
$$
for all real numbers $x, y, z$ satisfying $x^2 + y^2 + z^2 = 21$.
$$
|x - ky| + |y - kz| + |z - kx| \geq 7
$$
for all real numbers $x, y, z$ satisfying $x^2 + y^2 + z^2 = 21$.