lean_workbook_plus_9560

Proved

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

Prove that if $x + y + z = 6$ and $xy + yz + zx = 9$ ( $x,y,z\in\mathbb{R}$ ) then $0\le x,y,z\le 4$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9560 (x y z : ℝ) (h₁ : x + y + z = 6) (h₂ : x * y + y * z + z * x = 9) : 0 ≤ x ∧ x ≤ 4 ∧ 0 ≤ y ∧ y ≤ 4 ∧ 0 ≤ z ∧ z ≤ 4   :=  by sorry

Source

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

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