A weighted quadratic reciprocal upper bound at fixed sum three

Proved

WorkbookSource.base_35152

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

lean-workbooksource-checked

Let $a,b,c>0,a+b+c=3.$ Prove that

\frac{1}{2a^2+b^2+c^2}+\frac{1}{2b^2+c^2+a^2}+\frac{1}{2c^2+a^2+b^2}\le \frac{3}{4}

Source: InternLM Lean-Workbook, record lean_workbook_35152 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_35152 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (1 / (2 * a ^ 2 + b ^ 2 + c ^ 2) + 1 / (2 * b ^ 2 + c ^ 2 + a ^ 2) + 1 / (2 * c ^ 2 + a ^ 2 + b ^ 2)) ≤ (3 / 4)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35152; Apache-2.0

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