lean_workbook_plus_53644

⚠️ 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.

Prove that for any nonnegative real numbers $a,b,c,$ we have \n a) \n $\frac {a^2 + b^2 + c^2}{ab + bc + ca} + 15\sqrt {\frac {a^3b + b^3c + c^3a}{a^2b^2 + b^2c^2 + c^2a^2}} \ge \frac {47}{4}. \n b) \n$ \sqrt {\frac {a^2 + b^2 + c^2}{ab + bc + ca}} + \sqrt {\frac {3(a^3b + b^3c + c^3a)}{a^2b^2 + b^2c^2 + c^2a^2}} \ge 1 + \sqrt {3}. \n

Why this node was retired

The posted statement is

theorem lean_workbook_plus_53644 : ∀ a b c : ℝ, (a^2 + b^2 + c^2) / (a * b + b * c + c * a) + 15 * Real.sqrt ((a^3 * b + b^3 * c + c^3 * a) / (a^2 * b^2 + b^2 * c^2 + c^2 * a^2)) ≥ 47 / 4   :=  by sorry

Nonnegativity was omitted and zero denominators are admitted.

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

Proposed corrected statement

For a,b,c≥0 with ab+bc+ca>0, state and prove both source inequalities; the positive denominator condition also ensures a²b²+b²c²+c²a²>0. Do not include the all-zero 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.