A weighted sum of two squares bounds a normalized triple product

Proved

WorkbookSource.base_22767

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers .Prove that

(a+b)^2+\left(a+b-\frac{16}{3} \cdot c\right)^2 \geqslant \frac{200}{9} \cdot \frac{abc}{a+b+c}.

Source: InternLM Lean-Workbook, record lean_workbook_22767 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_22767 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b) ^ 2 + (a + b - 16 / 3 * c) ^ 2 ≥ 200 / 9 * (a * b * c) / (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_22767; Apache-2.0

View graph