lean_workbook_plus_8245

Proved

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

Given three positive real numbers $a,b,c$ such that following holds $a^2=b^2+bc$ , $b^2=c^2+ac$ Prove that $\frac{1}{c}=\frac{1}{a}+\frac{1}{b}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8245 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a^2 = b^2 + b * c) (hbc : b^2 = c^2 + c * a) : 1 / c = 1 / a + 1 / b   :=  by sorry

Source

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

View graph