lean_workbook_plus_63531

Proved

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

For $a,b>0,\frac{1}{a}+\frac{1}{b}=1.$ Prove that $\frac{ a^2}{a+2b }+\frac{ b^2 }{b+2a} \geq \frac{4}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63531 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : 1 / a + 1 / b = 1) : a^2 / (a + 2 * b) + b^2 / (b + 2 * a) ≥ 4 / 3   :=  by sorry

Source

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

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