A quadratic bound with a pairwise-product constraint

Proved

WorkbookSource.problem_32941

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

lean-workbooksource-checked

Let $a,$ $b$ and $c$ are non-negative numbers such that $ab+ac+bc=3.$ Prove that $a^2+b^2+c^2+15\geq6(a+b+c)$

Source: InternLM Lean-Workbook, record lean_workbook_32941 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_32941 (a b c : ℝ) (habc : a * b + b * c + c * a = 3) : a ^ 2 + b ^ 2 + c ^ 2 + 15 ≥ 6 * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32941; Apache-2.0

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