A mixed power sum lower bound at fixed sum two

Proved

WorkbookSource.base_36664

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

lean-workbooksource-checked

Let $a,b,c>0,a+b+c=2 .$ Prove that

a^2+b^3+c^3\geq \frac{28}{27}.

Source: InternLM Lean-Workbook, record lean_workbook_36664 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_36664 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 2) : a^2 + b^3 + c^3 ≥ 28 / 27  :=  by sorry

Source