A lower bound involving a square root

Proved

WorkbookSource.problem_28339

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $x^2 +2\sqrt{x+2}-3x \geq 2$ for $x\geq 2$ .

Source: InternLM Lean-Workbook, record lean_workbook_28339 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_28339 (x : ℝ) (h : x ≥ 2) : x^2 + 2 * Real.sqrt (x + 2) - 3 * x ≥ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28339; Apache-2.0

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