lean_workbook_plus_71076

⚠️ 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.

So we have $\frac{1}{r_{1}}+\frac{1}{r_{2}}+\frac{1}{r_{3}}= \frac{r_{1}r_{2}+r_{2}r_{3}+r_{3}r_{1}}{r_{1}r_{2}r_{3}}=9$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_71076  (r₁ r₂ r₃ : ℝ)
  (h₀ : r₁ ≠ 0 ∧ r₂ ≠ 0 ∧ r₃ ≠ 0)
  (h₁ : r₁ + r₂ + r₃ = 9)
  (h₂ : r₁ * r₂ * r₃ = 32) :
  1 / r₁ + 1 / r₂ + 1 / r₃ = 9   :=  by sorry

The reciprocal sum depends on the second elementary symmetric sum, not the sum of roots; the posted assumptions do not supply it.

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

Proposed corrected statement

Assume nonzero r_i and r₁r₂+r₂r₃+r₃r₁=9r₁r₂r₃. Then prove∑1/r_i=9. Recover the polynomial/Viète data justifying that relation instead of using∑r_i=9.

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.