The following question was a homework and I did not knew how to solve that So I asked my teacher he said the minimum value is achieved at $x = y =z$. the question is as follows:

**If $x$, $y$, $z$ are distinct positive real numbers, the minimum value of** 
$$\frac{x^2 (y + z) + y^2 (x + z) + z^2 (x + y)}{xyz}$$

I do not get it why is the solution at x = y = z . the question states "3 distinct real positive numbers" but x = y = z are not distinct numbers.

Also if the question was :

**The sum of $2$ distinct positive real numbers is $6$, what is the maximum value of their product?**

Would it be a number less than $9$ but not equal to $9$ and what would that number be ?