A sum bound under a pairwise-product constraint

Proved

WorkbookSource.problem_5159

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

inequalitieslean-workbooksource-checked

For real $a,b,c$ with $ab+ac+bc=3$ ,

a^2+b^2+c^2+5(ab+bc+ca)\ge6(a+b+c).

Source: InternLM Lean-Workbook, record lean_workbook_5159 (Apache-2.0). The complete source proposition is preserved.

Preamble

import Mathlib

Formal statement

theorem WorkbookSource.problem_5159 (a b c: ℝ) (hab : a * b + a * c + b * c = 3) : a ^ 2 + b ^ 2 + c ^ 2 + 5 * (a * b + b * c + c * a) ≥ 6 * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5159; Apache-2.0

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