lean_workbook_plus_26895

Proved

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

Let $x,y,z \in R$ and $x,y,z \not= 0$ and $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$ . Prove that: $\frac{yz}{x^2}+\frac{zx}{y^2}+\frac{xy}{z^2}=3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_26895 (x y z : ℝ) (hx : x ≠ 0) (hy : y ≠ 0) (hz : z ≠ 0) (h : 1/x + 1/y + 1/z = 0) : y * z / x ^ 2 + z * x / y ^ 2 + x * y / z ^ 2 = 3   :=  by sorry

Source

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

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