A comparison of weighted linear reciprocal sums
ProvedWorkbookSource.base_34373lean-workbooksource-checked
Let be positive real numbers. Prove that:
Source: InternLM Lean-Workbook, record lean_workbook_34373 (Apache-2.0). Complete source proposition preserved; proof developed independently.
Preamble
import Mathlib open Real Nat
Formal statement
theorem WorkbookSource.base_34373 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (a + 2 * b) + 1 / (b + 2 * c) + 1 / (c + 2 * a)) ≥ 4 * (1 / (3 * a + 4 * b + 5 * c) + 1 / (3 * b + 4 * c + 5 * a) + 1 / (3 * c + 4 * a + 5 * b)) := by sorry
Source