lean_workbook_plus_79170

Proved

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

Prove that for non-negative a, b, c\n\n1.\n $\frac{a+\sqrt{ab}}{2} \leq \sqrt{a \times \frac{a+b}{2}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79170 (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) :
  (a + Real.sqrt (a * b)) / 2 ≤ Real.sqrt (a * (a + b) / 2)   :=  by sorry

Source