lean_workbook_plus_77908

⚠️ 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 largest positive $p$ ( $p>1$ ) such, that $\forall a,b,c\in[\frac1p,p]$ the following inequality takes place\n$9(ab+bc+ca)(a^2+b^2+c^2)\geq(a+b+c)^4$\nmy guess is $\sqrt{4+3\sqrt{2}}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_77908 : ∀ p : ℝ, p > 1 ∧ (∀ a b c : ℝ, a ∈ Set.Icc (1 / p) p ∧ b ∈ Set.Icc (1 / p) p ∧ c ∈ Set.Icc (1 / p) p → 9 * (a * b + b * c + c * a) * (a ^ 2 + b ^ 2 + c ^ 2) ≥ (a + b + c) ^ 4) ↔ p ≤ Real.sqrt (4 + 3 * Real.sqrt 2)   :=  by sorry

Move p>1 outside the equivalence: for p>1, the universal box inequality holds iff p≤√(4+3√2).

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

Proposed corrected statement

Move p>1 outside the equivalence: for p>1, the universal box inequality holds iff p≤√(4+3√2).

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.