lean_workbook_plus_37661

Proved

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

Prove that \n\n $[5(a^2+b^2+c^2)-2(ab+bc+ca)]^2 \ge 15(a^4+b^4+c^4)+12abc(a+b+c)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37661 (a b c : ℝ) :
  (5 * (a ^ 2 + b ^ 2 + c ^ 2) - 2 * (a * b + b * c + c * a)) ^ 2 ≥
    15 * (a ^ 4 + b ^ 4 + c ^ 4) + 12 * a * b * c * (a + b + c)   :=  by sorry

Source

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

View graph