lean_workbook_plus_73433

⚠️ 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.

Given that $x_1, x_2$ are real solutions to the equation $x^2+a^2x+b=0$ while $x_3, x_4$ are real solutions to the equation $x^2+5ax+7=0$ such that $x_1-x_3=x_2-x_4=2$ , find the values of $a$ and $b$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_73433 (a b : ℝ) (x1 x2 x3 x4 : ℝ) (h1 : x1^2 + a^2 * x1 + b = 0) (h2 : x2^2 + a^2 * x2 + b = 0) (h3 : x3^2 + 5 * a * x3 + 7 = 0) (h4 : x4^2 + 5 * a * x4 + 7 = 0) (h5 : x1 - x3 = 2) (h6 : x2 - x4 = 2) : a = -1 ∧ b = -6   :=  by sorry

Require complete root pairs, using multiplicities or pairwise distinct roots as appropriate, and replace the proposed answer by a=4,b=−29.

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

Proposed corrected statement

Require complete root pairs, using multiplicities or pairwise distinct roots as appropriate, and replace the proposed answer by a=4,b=−29.

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.