A bilinear bound under fixed sum and squared norm

Proved

WorkbookSource.base_34479

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

lean-workbooksource-checked

Let $x, y,z$ be real numbers such that $x+y+z=2$ and $x^2+y^2+z^2=6$ . Prove that $(y-z)(x+y) \leq 9$

Source: InternLM Lean-Workbook, record lean_workbook_34479 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_34479 (x y z : ℝ) (h1 : x + y + z = 2) (h2 : x ^ 2 + y ^ 2 + z ^ 2 = 6) : (y - z) * (x + y) ≤ 9  :=  by sorry

Source