lean_workbook_plus_78956

Proved

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

Let $a,b,c>0$ and $a(a+2b+c)=2(b^2+2c^2).$ Prove that $\frac{a}{2b+c} \geq\frac{1}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78956 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * (a + 2 * b + c) = 2 * (b ^ 2 + 2 * c ^ 2)) : (a / (2 * b + c) ≥ 1 / 3)   :=  by sorry

Source

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

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