lean_workbook_plus_17180

Proved

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

Prove that $\frac{(x+y+z)^2}{(xy+yz+zx)(a+b)} \ge 3$ given $x,y,z,a,b$ are positive and $a+b=1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17180 (x y z a b : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (ha : 0 < a) (hb : 0 < b) (hab : a + b = 1) : (x + y + z) ^ 2 / (x * y + y * z + z * x) * (1 / (a + b)) ≥ 3   :=  by sorry

Source

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

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