# 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?

×