lean_workbook_plus_451

Proved

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

Show that: $9(a^{3} + 3b^{3} + 5c^{3})\geq(a^{2} + 3b^{2} + 5c^{2})(a + 3b + 5c)$ , for all $a,\ b,\ c\geq 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_451 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 9 * (a^3 + 3 * b^3 + 5 * c^3) ≥ (a^2 + 3 * b^2 + 5 * c^2) * (a + 3 * b + 5 * c)   :=  by sorry

Source

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

View graph