lean_workbook_plus_969

Proved

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

Prove that $(\frac {1}{x}+\frac{1}{y}+\frac {1}{z})^2 \ge 3(\frac {1}{xy}+\frac {1}{yz}+\frac {1}{zx})=3.(\frac {x+y+z}{xyz})$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_969 (x y z : ℝ) : (1 / x + 1 / y + 1 / z) ^ 2 ≥ 3 * (1 / (x * y) + 1 / (y * z) + 1 / (z * x))   :=  by sorry

Source