lean_workbook_plus_48884

Proved

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

Show that $(a - \sqrt{7} b)^2 > 0$ implies $a^2 + 7 b^2 > 2 \sqrt{7} a b$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_48884 (a b : ℝ) (h : (a - Real.sqrt 7 * b) ^ 2 > 0) :
  a ^ 2 + 7 * b ^ 2 > 2 * Real.sqrt 7 * a * b   :=  by sorry

Source