lean_workbook_plus_11032

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If $a,b,c$ are reals positives. Prove that \n

\frac{a^2}{b^2+2c^2}+\frac{b^2}{c^2+2a^2}+\frac{c^2}{a^2+2b^2}\ge 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11032 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a^2 / (b^2 + 2 * c^2) + b^2 / (c^2 + 2 * a^2) + c^2 / (a^2 + 2 * b^2)) ≥ 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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