lean_workbook_plus_2896

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Prove that for positive real numbers a,b,c, the following inequality holds: $3\sqrt[9]{\frac{9a(a+b)}{2(a+b+c)^{2}}}+\sqrt[3]{\frac{6bc}{(a+b)(a+b+c)}}\leq4$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_2896 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 3 * (9 * a * (a + b) / 2 * (a + b + c) ^ 2) ^ (1 / 9) + (6 * b * c / (a + b) / (a + b + c)) ^ (1 / 3) ≤ 4   :=  by sorry

Natural root exponents make the target4≤4. The first denominator is misparenthesized: division by2 followed by multiplication by(a+b+c)² replaces division by2(a+b+c)².

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Confirmed directly from the Lean text: the numeric-literal exponents carry no type ascription, so they elaborate at type ℕ where division truncates (^ (1 / 3) → ^0; ^ (1 / 9) → ^0).

Proposed corrected statement

For a,b,c>0 prove3·⁹√(9a(a+b)/(2(a+b+c)²))+∛(6bc/((a+b)(a+b+c)))≤4, with the complete intended denominator and genuine nonnegative roots.

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.