Prove $\sum_{t=1}^{T}\sqrt{x_t-1}$, where $x_t\ge 1$ and $\prod_{t=1}^{T}x_t\le T$, gets its maximum when $x_t=T^{1/T}$.
Preliminary idea: The square root is a concave function. Sum of concave functions is concave.
2026-04-03 06:34:39.1775198079
Why is sum of square root (given product) maximized with equal summands?
204 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in INEQUALITY
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