A quartic ratio with a triple-product correction

Proved

WorkbookSource.plus_19234

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

lean-workbooksource-checked

Let $a,b,c>0$ prove that

\frac{a^4+b^4+c^4}{ab+bc+ca}+\frac{9abc}{2(a+b+c)} \geqslant \frac{5}{6}(a^2+b^2+c^2).

Source: InternLM Lean-Workbook, record lean_workbook_plus_19234 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_19234 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^4 + b^4 + c^4) / (a * b + b * c + c * a) + (9 * a * b * c) / (2 * (a + b + c)) ≥ (5 / 6) * (a^2 + b^2 + c^2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_19234; Apache-2.0

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