lean_workbook_plus_32545

⚠️ 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.

Under the condition $x^4 + y^4 + z^4 = 1$ , find the maximum and minimum of $x^2 + y^2 + z^2$ , not by using Lagrange multiplier but elementarily , (if you can).

Why this node was retired

The posted statement is

theorem lean_workbook_plus_32545 (x y z : ℝ) (h : x ^ 4 + y ^ 4 + z ^ 4 = 1) :
  3 * Real.sqrt 3 / 2 ≤ x ^ 2 + y ^ 2 + z ^ 2 ∧ x ^ 2 + y ^ 2 + z ^ 2 ≤ Real.sqrt 3   :=  by sorry

Replace the lower bound by1 and retain the upper bound√3; include attainment at(±1,0,0) and at equal absolute coordinates3^(−1/4), respectively.

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

Proposed corrected statement

Replace the lower bound by1 and retain the upper bound√3; include attainment at(±1,0,0) and at equal absolute coordinates3^(−1/4), respectively.

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.