A cyclic cubic difference reciprocal bound at fixed sum three

Proved

WorkbookSource.base_6721

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers such that $a+b+c=3$ ,Show that $\frac{a^3-8a+8}{b+c}+\frac{b^3-8b+8}{c+a}+\frac{c^3-8c+8}{a+b}\ge \frac{3}{2}.$

Source: InternLM Lean-Workbook, record lean_workbook_6721 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6721 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c = 3) : (a^3 - 8 * a + 8) / (b + c) + (b^3 - 8 * b + 8) / (c + a) + (c^3 - 8 * c + 8) / (a + b) ≥ 3 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6721; Apache-2.0

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