lean_workbook_plus_12052

Proved

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

Let $a,b,c,d,x,y,z$ be positive reals with $a^2+b^2+c^2 = d^2$ . Show that $x^2+y^2+z^2 \ge \left( \dfrac{ ax+by+cz}{d} \right)^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12052 (a b c d x y z : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (habc : a * a + b * b + c * c = d * d) : x * x + y * y + z * z ≥ (a * x + b * y + c * z) ^ 2 / d ^ 2   :=  by sorry

Source

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

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