A cyclic squared linear ratio sum is at least eight
ProvedWorkbookSource.plus_36715lean-workbooksource-checked
Prove that if then $ \frac {(4a + b - c)^2}{2a^2 + (b + c)^2} + \frac {(4b + c - a)^2}{2b^2 + (c + a)^2} + \frac {(4c + a - b)^2}{2c^2 + (a + b)^2}\geq8.
Source: InternLM Lean-Workbook, record lean_workbook_plus_36715 (Apache-2.0). Complete source proposition preserved; proof developed independently.
Preamble
import Mathlib open Real Nat
Formal statement
theorem WorkbookSource.plus_36715 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (4 * a + b - c) ^ 2 / (2 * a ^ 2 + (b + c) ^ 2) + (4 * b + c - a) ^ 2 / (2 * b ^ 2 + (c + a) ^ 2) + (4 * c + a - b) ^ 2 / (2 * c ^ 2 + (a + b) ^ 2) ≥ 8 := by sorry
Source