lean_workbook_plus_39808

Proved

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

Let $a,\ b,\ c$ be real numbers such that $a < b < c,\ a + b + c = 0.$ Prove that $\frac {a^2 + b^2 + c^2}{(c - a)^2}< \frac{2}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39808 (a b c : ℝ) (h₁ : a < b ∧ b < c) (h₂ : a + b + c = 0) : (a^2 + b^2 + c^2) / (c - a)^2 < 2 / 3   :=  by sorry

Source