A two-term rational lower bound for three positive variables

Proved

WorkbookSource.base_2528

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers. Prove that $\frac{(a+b)^2}{c} + \frac{c^2}{a} \geq 4b$

Source: InternLM Lean-Workbook, record lean_workbook_2528 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2528 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a + b) ^ 2 / c + c ^ 2 / a ≥ 4 * b  :=  by sorry

Source