A weighted quadratic ratio sum is at least twenty-one

Proved

WorkbookSource.base_52341

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

lean-workbooksource-checked

For $a,b,c$ positive reals prove: $\frac{a^2+2b^2+4c^2}{bc} + \frac{b^2+2c^2+4a^2}{ca}+ \frac{c^2+2a^2+4b^2}{ab} \geq 21$

Source: InternLM Lean-Workbook, record lean_workbook_52341 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_52341 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + 2 * b^2 + 4 * c^2) / b / c + (b^2 + 2 * c^2 + 4 * a^2) / c / a + (c^2 + 2 * a^2 + 4 * b^2) / a / b ≥ 21  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52341; Apache-2.0

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