lean_workbook_plus_39182

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that: \n $x,y,z>0\Rightarrow (x+y+z)(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})\ge 7+\frac{2(x^2+y^2+z^2)}{xy+yz+zx}$ \n

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39182 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y + z) * (1 / x + 1 / y + 1 / z) ≥ 7 + 2 * (x ^ 2 + y ^ 2 + z ^ 2) / (x * y + y * z + z * x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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