A squared difference ratio sum bounds a normalized quadratic sum

Proved

WorkbookSource.plus_60608

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

lean-workbooksource-checked

For any positive real numbers $a,b,c$ we have the inequality $\frac{(b+c-a)^2}{17a^2+7(b+c)^2}+\frac{(c+a-b)^2}{17b^2+7(c+a)^2}+\frac{(a+b-c)^2}{17c^2+7(a+b)^2}\geq\frac{a^2+b^2+c^2}{5(a+b+c)^2}$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_60608 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_60608 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c - a) ^ 2 / (17 * a ^ 2 + 7 * (b + c) ^ 2) + (c + a - b) ^ 2 / (17 * b ^ 2 + 7 * (c + a) ^ 2) + (a + b - c) ^ 2 / (17 * c ^ 2 + 7 * (a + b) ^ 2) ≥ (a ^ 2 + b ^ 2 + c ^ 2) / (5 * (a + b + c) ^ 2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_60608; Apache-2.0

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