lean_workbook_plus_26459

Proved

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

Let $a,b,c>0$ and $a^2+b^2+c^2=2(ab+bc+ca).$ Prove that \n

\frac{a+kb}{c} \geq \frac{k}{k+1}

Where $k>0 .$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_26459 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b > c) (h : a^2 + b^2 + c^2 = 2 * (a * b + b * c + c * a)) (k : ℝ) (hk : k > 0) : (a + k * b) / c ≥ k / (k + 1)   :=  by sorry

Source

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

View graph