lean_workbook_plus_64728

⚠️ 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.

We have to minimize $ab + ac + bc$ given $abc = 12$ and $a + b + c = 7$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_64728 (a b c : ℝ) (h₁ : a + b + c = 7) (h₂ : a * b * c = 12) : a * b + b * c + a * c ≥ 12 ∧ ∃ a b c : ℝ, a + b + c = 7 ∧ a * b * c = 12 ∧ a * b + b * c + a * c = 12   :=  by sorry

The inserted minimum12 is unsupported and the all-real feasible set admits values below it.

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

Proposed corrected statement

Determine the infimum/range of ab+ac+bc for real a,b,c satisfying a+b+c=7,abc=12, or recover the source positivity restriction and solve that different minimization. Do not assert an attained minimum12 without derivation.

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.