Question 128
There are exactly three positive real numbers $k$ such that the function
$$
f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x}
$$
defined over the positive real numbers $x$ achieves its minimum value at exactly two positive real numbers $x$. Find the sum of these three values of $k$.
$$
f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x}
$$
defined over the positive real numbers $x$ achieves its minimum value at exactly two positive real numbers $x$. Find the sum of these three values of $k$.