lean_workbook_plus_7738

Proved

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

Let $a,b,c$ be three positive real numbers , prove that : $\frac{a}{b^2}+\frac{b}{c^2}+\frac{c}{a^2}\ge \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7738 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b ^ 2 + b / c ^ 2 + c / a ^ 2) ≥ (1 / a + 1 / b + 1 / c)   :=  by sorry

Source

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

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