lean_workbook_plus_6773

Proved

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

For $a,b>0$ , prove the following inequality: $8(a^2+2)^2(b^2+2)^2\ge 81(a+b)^2+36ab(a^2+2)(b^2+2)$ Also prove the equality holds if and only if $a=b=1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6773 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : 8 * (a^2 + 2)^2 * (b^2 + 2)^2 ≥ 81 * (a + b)^2 + 36 * a * b * (a^2 + 2) * (b^2 + 2)   :=  by sorry

Source

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

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