A quadratic reciprocal sum bounds twice the total

Proved

WorkbookSource.base_1552

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

lean-workbooksource-checked

Let $x, y, z$ be positive real numbers. Prove that $\frac{y^2 + z^2}{x}+\frac{z^2 + x^2}{y}+\frac{x^2 + y^2}{z}\ge 2(x + y + z)$ .

Source: InternLM Lean-Workbook, record lean_workbook_1552 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1552 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (y ^ 2 + z ^ 2) / x + (z ^ 2 + x ^ 2) / y + (x ^ 2 + y ^ 2) / z ≥ 2 * (x + y + z)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1552; Apache-2.0

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