lean_workbook_plus_65530

Proved

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

$\implies{ (ax + by +cz )^{2} \leq{ (a^{2} +b^{2}+c^{2})(x^{2} +y^{2}+z^{2}) }}$ , equality when $\frac{a}{x}=\frac{b}{y}=\frac{c}{z}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_65530 {a b c x y z : ℝ} :
  (a * x + b * y + c * z) ^ 2 ≤ (a ^ 2 + b ^ 2 + c ^ 2) * (x ^ 2 + y ^ 2 + z ^ 2)   :=  by sorry

Source