A cyclic quadratic reciprocal sum with a product correction at fixed sum six

Proved

WorkbookSource.base_4242

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c=6$ . Prove that $\frac{a^{2}}{b}+\frac{b^{2}}{c}+\frac{c^{2}}{a}+3abc\geq 24$

Source: InternLM Lean-Workbook, record lean_workbook_4242 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4242 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 6) : a^2 / b + b^2 / c + c^2 / a + 3 * a * b * c ≥ 24  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4242; Apache-2.0

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