lean_workbook_plus_67450

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Solve the system of equations: \n $\begin{cases}x^2+1+y(x+y)=48\ (x^2+1)(x+y-2)=y \end{cases}$\n

Why this node was retired

The posted statement is

theorem lean_workbook_plus_67450 (x y : ℝ) (h₁ : x^2 + 1 + y * (x + y) = 48) (h₂ : (x^2 + 1) * (x + y - 2) = y) : x = 5 ∧ y = 12   :=  by sorry

The given pair is not a solution, while the accepted proof establishes a genuine solution by continuity.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Restore the task “find all real solutions of the two displayed equations”; remove the invented answer(5,12). A complete replacement solution set has not been established in this audit.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.