lean_workbook_plus_14646

Disproved

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

Prove that for all $x > 0$ , $\sqrt{x + 2\sqrt{x - 1}} + \sqrt{x - 2\sqrt{x - 1}} = 2\sqrt{x - 1}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14646 : ∀ x > 0, Real.sqrt (x + 2 * Real.sqrt (x - 1)) + Real.sqrt (x - 2 * Real.sqrt (x - 1)) = 2 * Real.sqrt (x - 1)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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