A symmetric quadratic ratio sum is at least one

Proved

WorkbookSource.base_6985

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

lean-workbooksource-checked

Given $x,y,z>0$ , prove that $\frac{x^2}{y^2+z^2+yz}+\frac{y^2}{z^2+x^2+zx}+\frac{z^2}{x^2+y^2+xy}\geq1$ .

Source: InternLM Lean-Workbook, record lean_workbook_6985 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6985 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) : (x^2 / (y^2 + z^2 + y * z) + y^2 / (z^2 + x^2 + z * x) + z^2 / (x^2 + y^2 + x * y)) ≥ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6985; Apache-2.0

View graph