A normalized pairwise-product bound

Proved

WorkbookSource.problem_52170

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

lean-workbooksource-checked

prove that $\frac {3(ab + bc + ca)}{(a + b + c)^2}\leq 1$ where $a, b, c$ are positive numbers.

Source: InternLM Lean-Workbook, record lean_workbook_52170 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_52170 (a b c : ℝ) : 3 * (a * b + b * c + c * a) / (a + b + c) ^ 2 ≤ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52170; Apache-2.0

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