lean_workbook_plus_8956

⚠️ 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 all real numbers $k>-2$ such that the inequality $\frac{x}{x+y+kz}+\frac{y}{y+z+kx}+\frac{z}{z+x+ky}\geq\frac{3}{k+2}$ holds for all nonnegative $x,y$ and $z$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_8956 (k : ℝ) (h : k > -2) : ∀ x y z : ℝ, (x ≥ 0 ∧ y ≥ 0 ∧ z ≥ 0 → x / (x + y + k * z) + y / (y + z + k * x) + z / (z + x + k * y) ≥ 3 / (k + 2))   :=  by sorry

The correct admissible parameter set is not determined by the accepted zero-boundary counterexample.

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 find-all-k classification and exclude the zero tuple and any zero denominators from the ordinary fractions. Remove the assertion that every k>−2 works.

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.