An Inequality Made Up Of Greek Alphabets
Calculus
Level
5
Let \(0<\alpha,\beta,\gamma<\frac{1}{2}\) be real numbers with \(\alpha+\beta+\gamma=1.\) The minimum value of \(\delta\) which satisfies the inequality
\[\alpha^3+\beta^3+\gamma^3+4\alpha\beta\gamma \leq \delta\]
can be expressed in the form \( \frac{a}{b} \), where \(a\) and \(b\) are positive coprime integers. Find \(a+b\).
by
Victor Loh