Prove2Me

A weighted sum of three real squares

Proved
WorkbookSource.problem_40760

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

lean-workbooksource-checked

For real x,yx,y,

3(x+23)2+6(y+13)2+(x−2y)2≥0.3\left(x+\frac23\right)^2+6\left(y+\frac13\right)^2+(x-2y)^2\ge0.

Source: InternLM Lean-Workbook, record lean_workbook_40760 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_40760 (x y : ℝ) : (3 * (x + 2 / 3) ^ 2 + 6 * (y + 1 / 3) ^ 2 + (x - 2 * y) ^ 2) ≥ 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_40760; Apache-2.0

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