benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let a,b,c,d be real numbers such that a²+b²+c²+d²=1. Determine the minimum value of (a−b)(b−c)(c−d)(d−a) and determine all values of (a,b,c,d) such that the minimum value is achiev…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let a,b,c,da, b, c, d be real numbers such that a2+b2+c2+d2=1a^{2}+b^{2}+c^{2}+d^{2}=1. Determine the minimum value of (a−b)(b−c)(c−d)(d−a)(a-b)(b-c)(c-d)(d-a) and determine all values of (a,b,c,d)(a, b, c, d) such that the minimum value is achieved.
Plain-text mathematical notation (without MathML)
Let a,b,c,d be real numbers such that a²+b²+c²+d²=1. Determine the minimum value of (a−b)(b−c)(c−d)(d−a) and determine all values of (a,b,c,d) such that the minimum value is achieved.
Original LaTeX notation
Let $a, b, c, d$ be real numbers such that $a^{2}+b^{2}+c^{2}+d^{2}=1$. Determine the minimum value of $(a-b)(b-c)(c-d)(d-a)$ and determine all values of $(a, b, c, d)$ such that the minimum value is achieved.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

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. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
e229db1f-9291-5b84-a9fe-58598550933f
task_key
test--e229db1f-9291-5b84-a9fe-58598550933f
task_revision_id
1
config / split
/ test

Official source

initial import