lean_workbook_plus_80727

⚠️ 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 this system of equations in $R$ : \n $\begin {cases} x^3+ 2x^2y = (2x + 1)\sqrt{2x + y} \ 2x^3 + 2y\sqrt {2x + y} = 2y^2 + xy + 3x + 1 \end {cases}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_80727 (x y : ℝ) (h₁ : x^3 + 2*x^2*y = (2*x + 1)*Real.sqrt (2*x + y)) (h₂ : 2*x^3 + 2*y*Real.sqrt (2*x + y) = 2*y^2 + x*y + 3*x + 1) : x = 1 ∧ y = 0   :=  by sorry

The inserted root is wrong and the domain of the real radical is missing.

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

Proposed corrected statement

Find all real solutions of the two source equations with2x+y≥0 explicitly imposed, using the nonnegative square root. Do not retain the unsupported pair(1,0); the totalized negative-radicand extensions belong to a different problem.

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.