A weighted linear square bounds a pair-product sum

Proved

WorkbookSource.base_28742

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Give $x+y+z=1$ . Prove that: $44(xy+yz+xz) \leq (3x+4y+5z)^2$

Source: InternLM Lean-Workbook, record lean_workbook_28742 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28742 (x y z : ℝ) (h : x + y + z = 1) :
  44 * (x * y + y * z + x * z) ≤ (3 * x + 4 * y + 5 * z) ^ 2  :=  by sorry

Source