lean_workbook_plus_589

⚠️ 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 the values of $a, b, c$ when $a+b+c=1, ab+bc+ca=\frac{1}{4}, abc=\frac{1}{72}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_589 (a b c : ℝ) (ha : a + b + c = 1) (hb : a * b + b * c + c * a = 1 / 4) (hc : a * b * c = 1 / 72) : a = 1 / 2 ∧ b = 1 / 3 ∧ c = 1 / 6   :=  by sorry

The supplied triple does not even have the required product; an explicit radical parametrization is not established here.

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

Proposed corrected statement

Restore the complete unordered real-triple classification, equivalently permutations of the three roots of t³−t²+t/4−1/72. Remove the invented ordered triple.

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.