A weighted quadratic reciprocal sum upper bound

Proved

WorkbookSource.base_29975

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

lean-workbooksource-checked

Let $a,b$ be positive real numbers . Prove that $\frac{1}{a^2+b^2}+\frac{7}{a^2+49b^2}\leq\frac{2}{3ab}$

Source: InternLM Lean-Workbook, record lean_workbook_29975 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29975 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : 1 / (a ^ 2 + b ^ 2) + 7 / (a ^ 2 + 49 * b ^ 2) ≤ 2 / (3 * a * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29975; Apache-2.0

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