lean_workbook_plus_18273

⚠️ 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 $a, b, c \in \mathbb{R}$, solve the following system of equations:\n\n1. $a + b + c = 2$\n2. $ab + bc + ac = -7$\n3. $abc = -14$\n\nFind the values of $a$, $b$, and $c$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_18273 (a b c : ℝ) (h₁ : a + b + c = 2) (h₂ : a * b + b * c + a * c = -7) (h₃ : a * b * c = -14) : a = 2 ∧ b = -3.5 ∧ c = -1   :=  by sorry

The inserted ordered triple is wrong and ignores permutation symmetry.

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

Proposed corrected statement

Prove the solutions are precisely all permutations of(2,√7,−√7), using the factorization(t−2)(t²−7).

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.