A cyclic linear ratio upper bound by squared symmetric forms

Proved

WorkbookSource.base_50317

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

lean-workbooksource-checked

For $a, b, c>0$ prove that $\frac{a+2b}{a+b}+\frac{b+2c}{b+c}+\frac{c+2a}{c+a}\le\frac{9}{2}\left(\frac{a^2+b^2+c^2}{ab+bc+ca}\right)^2$

Source: InternLM Lean-Workbook, record lean_workbook_50317 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_50317 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + 2 * b) / (a + b) + (b + 2 * c) / (b + c) + (c + 2 * a) / (c + a) ≤ (9 / 2) * ((a ^ 2 + b ^ 2 + c ^ 2) / (a * b + b * c + c * a)) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_50317; Apache-2.0

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