lean_workbook_plus_7068

Proved

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

Let be $a,b,c,d\in \mathbb{R}_+$ such that $abcd=1$ . Prove that : \n\n $8+(a^2+b^2)(c^2+d^2)\ge 3(a+b)(c+d)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7068 (a b c d : ℝ) (hab : a * b * c * d = 1) : 8 + (a^2 + b^2) * (c^2 + d^2) ≥ 3 * (a + b) * (c + d)   :=  by sorry

Source