Inspired by Lakshya Sinha

Algebra Level 4

If \(a_1^3+a_2^3+\ldots+a_8^3\geq{8}\) for non-negative real \(a_k\), what is the minimal value of \(a_1+a_2+\ldots+a_8\)?

Bonus: What is the minimum (or infimum) of \(a_1+a_2+\cdots+a_8\) if the \(a_k\) are arbitrary real numbers?


Inspiration.

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