Extrapolating a weighted linear system

Proved

WorkbookSource.problem_1160

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

lean-workbooksource-checked

Let $a$ , $b$ , $c$ , and $d$ be real numbers such that $a+4b+9c+16d=25$ $4a+9b+16c+25d=36$ $9a+16b+25c+36d=49$ Compute $16a+25b+36c+49d$ .

Source: InternLM Lean-Workbook, record lean_workbook_1160 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_1160 (a b c d : ℝ) (ha : a + 4 * b + 9 * c + 16 * d = 25) (hb : 4 * a + 9 * b + 16 * c + 25 * d = 36) (hc : 9 * a + 16 * b + 25 * c + 36 * d = 49) : 16 * a + 25 * b + 36 * c + 49 * d = 64  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1160; Apache-2.0

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