lean_workbook_plus_57668

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If $a,b,c$ are positive reals and $a^2+b^2+c^2=3$ , then $ab+bc+ca\leq 1$ holds?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57668 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 ∧ a^2 + b^2 + c^2 = 3 → a * b + b * c + c * a ≤ 1   :=  by sorry

Source