lean_workbook_plus_64070

Proved

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

If $x,y,z>0$ prove that: \n $\frac{y+z}{x}+\frac{z+x}{y}+\frac{x+y}{z}\ge 3(1+\frac{x^2+y^2+z^2}{xy+yz+zx})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64070 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (y + z) / x + (z + x) / y + (x + y) / z >= 3 * (1 + (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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