A two-variable quadratic inequality

Proved

WorkbookSource.base_9749

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $x, y >0 .$ Prove that

3x^2 + y^2 + 1 \geq \frac{6}{5}(x^2 + xy + 2x)

Source: InternLM Lean-Workbook, record lean_workbook_9749 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9749 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : 3 * x ^ 2 + y ^ 2 + 1 ≥ 6 / 5 * (x ^ 2 + x * y + 2 * x)  :=  by sorry

Source