A cyclic quadratic ratio with a triple-product correction

Proved

WorkbookSource.plus_21366

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

lean-workbooksource-checked

Let $a,b,c>0$ which satisfy: $a+b+c =3$ . Prove that: $\frac{a^2}{b} + \frac{b^2}{c}+\frac{c^2}{a} +3abc \ge 6$ . Hope that this inequality have a nice solution

Source: InternLM Lean-Workbook, record lean_workbook_plus_21366 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_21366 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a^2 / b + b^2 / c + c^2 / a + 3 * a * b * c ≥ 6   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_21366; Apache-2.0

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