lean_workbook_plus_77892

Proved

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

Let $x,y,z$ be positive reals such that $\sqrt{a}=x(y-z)^2$ , $\sqrt{b}=y(z-x)^2$ and $\sqrt{c}=z(x-y)^2$ . Prove that $a^2+b^2+c^2 \geq 2(ab+bc+ca)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77892 (a b c x y z : ℝ) (ha : a = x * (y - z) ^ 2) (hb : b = y * (z - x) ^ 2) (hc : c = z * (x - y) ^ 2) : a ^ 2 + b ^ 2 + c ^ 2 ≥ 2 * (a * b + b * c + c * a)   :=  by sorry

Source

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

View graph