ThmDex – An index of mathematical definitions, results, and conjectures.
F12488
Formulation 0
Let $a, b, c \in (0, \infty)$ each be a D5407: Positive real number such that
(i) \begin{equation} 2 a + 2 b = c \end{equation}
Then
(1) \begin{equation} a b \leq \left( \frac{c}{4} \right)^2 \end{equation}
(2) \begin{equation} a b = \left( \frac{c}{4} \right)^2 \quad \iff \quad a = b \end{equation}