A cyclic ratio bound involving the normalized quadratic sum

Proved

WorkbookSource.base_15808

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

lean-workbooksource-checked

For positives $a$ , $b$ and $c$ prove that: $2\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)+1\geq\frac{21(a^2+b^2+c^2)}{(a+b+c)^2}$

Source: InternLM Lean-Workbook, record lean_workbook_15808 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15808 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 * (a / b + b / c + c / a) + 1 ≥ 21 * (a ^ 2 + b ^ 2 + c ^ 2) / (a + b + c) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15808; Apache-2.0

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