A quadratic form as a sum of squares

Proved

WorkbookSource.problem_51213

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c$ in $R^3$ . Then prove that $a^2+4b^2+8c^2\geq(3ab+4bc+2ac)$

Source: InternLM Lean-Workbook, record lean_workbook_51213 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_51213 (a b c : ℝ) : a ^ 2 + 4 * b ^ 2 + 8 * c ^ 2 ≥ 3 * a * b + 4 * b * c + 2 * a * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_51213; Apache-2.0

View graph