A shifted cyclic quadratic ratio sum is at most three seventeenths

Proved

WorkbookSource.base_55370

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

lean-workbooksource-checked

If $a, b, c>0, a+b+c=3$ prove that $\sum_{cyc}{\frac{a^2}{7a^2+9a+bc}}\le\frac{3}{17}$

Source: InternLM Lean-Workbook, record lean_workbook_55370 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_55370 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a^2 / (7 * a^2 + 9 * a + b * c) + b^2 / (7 * b^2 + 9 * b + c * a) + c^2 / (7 * c^2 + 9 * c + a * b) ≤ 3 / 17  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55370; Apache-2.0

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