A cyclic reciprocal-power comparison at fixed sum three

Proved

WorkbookSource.base_36975

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

lean-workbooksource-checked

If ${x}$ , $y$ and $z>0$ satisfies $x+y+z=3$ , show that $\frac{x}{y^2}+\frac{y}{z^2}+\frac{z}{x^2}\ge \frac{x^2}{y}+\frac{y^2}{z}+\frac{z^2}{x}$ .

Source: InternLM Lean-Workbook, record lean_workbook_36975 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_36975 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 3) : (x / y ^ 2 + y / z ^ 2 + z / x ^ 2) ≥ (x ^ 2 / y + y ^ 2 / z + z ^ 2 / x)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_36975; Apache-2.0

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