lean_workbook_plus_28289

Proved

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

Let $a,\,b,\,c$ are positive real numbers \n(1) Prove that \n $\frac{b+c}{a}+\frac{a^2}{bc} \geqslant 3 + \frac{(c-a)^2}{c(a+b)}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_28289 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c) / a + a ^ 2 / (b * c) ≥ 3 + (c - a) ^ 2 / (c * (a + b))   :=  by sorry

Source

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

View graph