Prove2Me

A weighted linear numerator over squared sums lower bound

Proved
WorkbookSource.base_52024

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

lean-workbooksource-checked

For positive real numbers a,b,c.a, b, c. Prove that 45a+b+9c(c+2a)2+45b+c+9a(a+2b)2+45c+a+9b(b+2c)2≥55a+b+c\frac{45a+b+9c}{(c+2a)^2}+\frac{45b+c+9a}{(a+2b)^2}+\frac{45c+a+9b}{(b+2c)^2}\geq \frac{55}{a+b+c}

Source: InternLM Lean-Workbook, record lean_workbook_52024 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_52024 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (45 * a + b + 9 * c) / (c + 2 * a) ^ 2 + (45 * b + c + 9 * a) / (a + 2 * b) ^ 2 + (45 * c + a + 9 * b) / (b + 2 * c) ^ 2 ≥ 55 / (a + b + c)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52024; Apache-2.0

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