lean_workbook_plus_16498

Proved

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

Let $a,b,c>0$ and $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=2.$ Prove that

\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}=a+b+c

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16498 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (b + c) + b / (c + a) + c / (a + b) = 2 → a ^ 2 / (b + c) + b ^ 2 / (c + a) + c ^ 2 / (a + b) = a + b + c)   :=  by sorry

Source

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

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