lean_workbook_plus_37649

Proved

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

Prove that for positive real numbers a and b, $(a^{2}+b+\frac{3}{4})(b^{2}+a+\frac{3}{4})\geq(a+b+\frac{1}{2})^2.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37649 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (a^2 + b + 3 / 4) * (b^2 + a + 3 / 4) ≥ (a + b + 1 / 2)^2   :=  by sorry

Source