lean_workbook_plus_70469

⚠️ 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.

Find polynomial function $P(x)$ $\forall x\in\mathbb{R}\neq 0$ such that: $2\left [ P(x)-P\left ( \frac{1}{x} \right ) \right ]^2+3P(x^2)P\left ( \frac{1}{x^2} \right )=0$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_70469 (x : ℝ) (hx : x ≠ 0) (f : ℝ → ℝ) (hf: f = fun x ↦ x^3 + 1/x^3) :  2 * (f x - f (1/x))^2 + 3 * f (x^2) * f (1/(x^2)) = 0   :=  by sorry

An unsupported rational function was substituted for the sought polynomial and fails the equation at1.

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 polynomials P∈ℝ[X] for which 2(P(x)−P(1/x))²+3P(x²)P(1/x²)=0 for every nonzero real x. Do not insert x³+x^(−3), which is not a polynomial.

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.