Factoring a quadratic inequality

Proved

WorkbookSource.problem_29312

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

lean-workbooksource-checked

denote by : $\frac{x}{y}+\frac{y}{x}=t$ , then : $t^{2}-2+4\geq 3t\Leftrightarrow (t-1)(t-2)\geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_29312 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_29312 (x y t : ℝ) (hx: x ≠ 0 ∧ y ≠ 0) (h : t = x/y + y/x) :  t^2 - 2 + 4 ≥ 3 * t ↔ (t - 1) * (t - 2) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29312; Apache-2.0

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