lean_workbook_plus_57756

Proved

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

If $a,b,c>0$ prove that \n\n $a^5+b^5+c^5\geq abc\left(a^2+b^2+c^2+\frac{2}{3}(a-b)^2\right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57756 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^5 + b^5 + c^5 ≥ a * b * c * (a^2 + b^2 + c^2 + (2 / 3) * (a - b)^2)   :=  by sorry

Source

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

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