A two-variable quadratic and quartic inequality

Proved

WorkbookSource.problem_16745

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

I’m not sure but one similar inequality I think is true is $a^2 + b^2 \ge ab(2-ab)$ for an real a, b.

Source: InternLM Lean-Workbook, record lean_workbook_16745 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_16745 (a b : ℝ) : a^2 + b^2 ≥ a * b * (2 - a * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16745; Apache-2.0

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