lean_workbook_plus_82102

Proved

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

proofwiki

If $x,y,z>0$ and $x+y+z=4$ , what is the maximum value of $xy+yz+xz$ ?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82102 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 4) : (x * y + y * z + z * x) ≤ 16/3 ∧ (∃ x y z : ℝ, (x * y + y * z + z * x) = 16/3)   :=  by sorry

Source

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

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