A sum-of-squares bound from a quadratic constraint

Proved

WorkbookSource.problem_10967

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

lean-workbooksource-checked

Prove that $a^2+b^2+c^2 \ge 12$ given $a,b,c>0$ and $3(a^2+b^2+c^2)+2(a+b+c)=48$ .

Source: InternLM Lean-Workbook, record lean_workbook_10967 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_10967 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0): 3 * (a ^ 2 + b ^ 2 + c ^ 2) + 2 * (a + b + c) = 48 → a ^ 2 + b ^ 2 + c ^ 2 ≥ 12  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10967; Apache-2.0

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