lean_workbook_plus_106

Proved

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

Since $(a+b+c)^{2}=(a+2b)(a+2c)+(b-c)^{2}$ it follows that \n $\frac{a+b+c}{a+2c}=\frac{a+2b}{a+b+c}+\frac{(b-c)^{2}}{(a+2c)(a+b+c)}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_106 :  ∀ a b c : ℝ, (a + b + c) ^ 2 = (a + 2 * b) * (a + 2 * c) + (b - c) ^ 2   :=  by sorry

Source