lean_workbook_plus_64455

⚠️ 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.

What is the value of $r^2+s^2$ if the $r,s$ are the roots of $x^2-3x+1=0$ ?

Why this node was retired

The posted statement is

theorem lean_workbook_plus_64455 (r s : ℝ) (hr : r^2 - 3 * r + 1 = 0) (hs : s^2 - 3 * s + 1 = 0) : r^2 + s^2 = 6   :=  by sorry

The wrong answer6 is inserted, and two independent root hypotheses do not enforce that r,s list both roots.

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

Proposed corrected statement

Let r,s be the two roots counted with multiplicity of x²−3x+1 (equivalently r+s=3,rs=1); prove r²+s²=7.

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.