A five-variable squared-sum bound under a product relation

Proved

WorkbookSource.base_3168

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c,d,e$ be real numbers such that $ab+bc+ca=20de$ . Prove that $13(a^2+b^2+c^2+d^2+e^2)\ge 3(a+b+c+d+e)^2$ .

Source: InternLM Lean-Workbook, record lean_workbook_3168 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3168 (a b c d e : ℝ) (h : a * b + b * c + c * a = 20 * d * e) :
  13 * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 + e ^ 2) ≥ 3 * (a + b + c + d + e) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3168; Apache-2.0

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