lean_workbook_plus_32272

Proved

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

Let $a,b,c$ be positive real numbers. Prove that $\frac{a} {5a^2+(b+c)^2} \leq\frac{5a+2(b+c)}{9(a+b+c)^2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32272 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (5 * a ^ 2 + (b + c) ^ 2) ≤ (5 * a + 2 * (b + c)) / (9 * (a + b + c) ^ 2))   :=  by sorry

Source

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

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