Recovering a product from two power sums

Proved

WorkbookSource.plus_51038

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

lean-workbooksource-checked

From $x^2+y^2=27$ , we have $(x^2+y^2)^2=x^4+y^4+2x^2y^2=729$ and using $x^4+y^4=487$ , we have $2x^2y^2=729-487=242$ and $(xy)^2=121$ and since $x,y>0$ , we have $xy=11$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_51038 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_51038  (x y : ℝ)
  (h₀ : 0 < x ∧ 0 < y)
  (h₁ : x^2 + y^2 = 27)
  (h₂ : x^4 + y^4 = 487) :
  x * y = 11   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_51038; Apache-2.0

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