Rescaling a quadratic-cubic equation

Proved

WorkbookSource.problem_20727

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

lean-workbooksource-checked

If $x=2a, y=2b, z=2c,$ then $x^2+y^2+z^2=2xyz\implies (2a)^2+(2b)^2+(2c)^2=2.2a.2b.2c=16abc$ $\Rightarrow 4(a^2+b^2+c^2)=16abc.$

Source: InternLM Lean-Workbook, record lean_workbook_20727 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_20727  (a b c : ℝ)
  (x y z : ℝ)
  (h₀ : x = 2 * a)
  (h₁ : y = 2 * b)
  (h₂ : z = 2 * c)
  (h₃ : x^2 + y^2 + z^2 = 2 * x * y * z) :
  4 * (a^2 + b^2 + c^2) = 16 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20727; Apache-2.0

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