A squared reciprocal-sum bound for a symmetric product

Proved

WorkbookSource.base_15913

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

lean-workbooksource-checked

If $x,y,z>0$ prove: $\frac{(y+z)^2}{x^2}+\frac{(z+x)^2}{y^2}+\frac{(x+y)^2}{z^2}+28\ge\frac{5(x+y)(y+z)(z+x)}{xyz}$

Source: InternLM Lean-Workbook, record lean_workbook_15913 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15913 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (y + z) ^ 2 / x ^ 2 + (z + x) ^ 2 / y ^ 2 + (x + y) ^ 2 / z ^ 2 + 28 ≥ 5 * (x + y) * (y + z) * (z + x) / (x * y * z)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15913; Apache-2.0

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