A quadratic lower bound under a quartic constraint

Proved

WorkbookSource.base_38006

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Two real numbers $a$ and $b$ are given, such that $a^4 + b^4 +a^2b^2 = 60.$ Prove that

4a^2 + 4b^2 - ab \ge 30

Source: InternLM Lean-Workbook, record lean_workbook_38006 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38006 (a b : ℝ) (h : a^4 + b^4 + a^2 * b^2 = 60) :
  4 * a^2 + 4 * b^2 - a * b ≥ 30  :=  by sorry

Source