ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F12492 on R5211: Tight upper bound to a product of three unsigned real numbers
F12492
Formulation 0
Let $x, y, z \in [0, \infty)$ each be an D4767: Unsigned real number.
Then
(1) \begin{equation} x y z \leq \left( \frac{x + y + z}{3} \right)^3 \end{equation}
(2) \begin{equation} x y z = \left( \frac{x + y + z}{3} \right)^3 \quad \iff\quad x = y = z \end{equation}