A mixed quadratic reciprocal upper bound

Proved

WorkbookSource.base_32573

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

lean-workbooksource-checked

Let $a, b, c>0$ . Prove that $\frac{a+b}{5c^2+ab}+\frac{b+c}{5a^2+bc}+\frac{c+a}{5b^2+ca}\le\frac{a^2+b^2+c^2}{3abc}$

Source: InternLM Lean-Workbook, record lean_workbook_32573 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_32573 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b) / (5 * c ^ 2 + a * b) + (b + c) / (5 * a ^ 2 + b * c) + (c + a) / (5 * b ^ 2 + c * a) ≤ (a ^ 2 + b ^ 2 + c ^ 2) / (3 * a * b * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32573; Apache-2.0

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