A weighted linear and quadratic constraint bounds the sum

Proved

WorkbookSource.problem_2789

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers such that $a+2b+c=a^2+2b^2+c^2.$ Prove that

a+2b+c \leq 4

Source: InternLM Lean-Workbook, record lean_workbook_2789 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_2789 (a b c : ℝ) (h : a + 2 * b + c = a^2 + 2 * b^2 + c^2) : a + 2 * b + c ≤ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2789; Apache-2.0

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