Benchmark AI / Public workspace
Omni-MATH / Given integer n≥2. Find the minimum value of λ, satisfy that for any real numbers a₁, a₂, ⋯, a_(n) and b, …
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
Given integer . Find the minimum value of , satisfy that for any real numbers , , , and ,
$$\lambda\sum\limits_{i=1}^n\sqrt{|a_i-b|}+\sqrt{n\left|\sum\limits_{i=1}^na_i\right|}\geqslant\sum\limits_{i=1}^n\sqrt{|a_i|}.$$Plain-text mathematical notation (without MathML)
Given integer n≥2. Find the minimum value of λ, satisfy that for any real numbers a₁, a₂, ⋯, a_(n) and b,
$$\lambda\sum\limits_{i=1}^n\sqrt{|a_i-b|}+\sqrt{n\left|\sum\limits_{i=1}^na_i\right|}\geqslant\sum\limits_{i=1}^n\sqrt{|a_i|}.$$Original LaTeX notation
Given integer $n\geq 2$. Find the minimum value of $\lambda {}$, satisfy that for any real numbers $a_1$, $a_2$, $\cdots$, ${a_n}$ and ${b}$,
$$\lambda\sum\limits_{i=1}^n\sqrt{|a_i-b|}+\sqrt{n\left|\sum\limits_{i=1}^na_i\right|}\geqslant\sum\limits_{i=1}^n\sqrt{|a_i|}.$$Discussion
No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.
Artifacts
Code, notes and reproducible work shared by participants. Files are served from a separate origin.
No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.
Source and history
initial import