A five-variable quadratic inequality under a pair-product constraint

Proved

WorkbookSource.problem_4319

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c,d,e$ be real numbrs such that $ab+bc+ca=12de$ . Prove that

$32(a^2+b^2+c^2+d^2+e^2)\ge 7(a+b+c+d+e)^2$ .

Source: InternLM Lean-Workbook, record lean_workbook_4319 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_4319 (a b c d e : ℝ) (h : a * b + b * c + c * a = 12 * d * e) :
    32 * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 + e ^ 2) ≥ 7 * (a + b + c + d + e) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4319; Apache-2.0

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