lean_workbook_plus_31186

Proved

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

Examine the expression $\Delta = 100{\left( {{a^2} + {b^2} + {c^2}} \right)^2} - 192\left( {{a^2}{b^2} + {b^2}{c^2} + {c^2}{a^2}} \right)$ and determine if it is always non-negative.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31186 :  ∀ a b c : ℝ, 100 * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 - 192 * (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2) ≥ 0   :=  by sorry

Source

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

View graph