A quadratic bound above one

Proved

WorkbookSource.problem_23650

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

lean-workbooksource-checked

Let $x=\frac{a^2+b^2+c^2}{ab+bc+ca}\geq 1$ . Remain to prove:

$x^2+\frac{1}{9}(2-x)(11+4x) \geq \frac{2}{3}x+2$

Source: InternLM Lean-Workbook, record lean_workbook_23650 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_23650 (x : ℝ) (hx : x ≥ 1) : x^2 + 1/9 * (2 - x) * (11 + 4 * x) ≥ 2/3 * x + 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23650; Apache-2.0

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