A cyclic pair-product ratio sum is at most one
ProvedWorkbookSource.base_35524lean-workbooksource-checked
Prove that $ ab/(a^{2} + 2b^{2}) + bc/(b^{2} + 2c^{2}) + ca/(c^{2} + 2a^{2}) \leq 1 $ for positive numbers $ a, b, c $.
Source: InternLM Lean-Workbook, record lean_workbook_35524 (Apache-2.0). Complete source proposition preserved; proof developed independently.
Preamble
import Mathlib open Real Nat
Formal statement
theorem WorkbookSource.base_35524 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a * b / (a ^ 2 + 2 * b ^ 2) + b * c / (b ^ 2 + 2 * c ^ 2) + c * a / (c ^ 2 + 2 * a ^ 2) ≤ 1 := by sorry
Source