A squared pairwise ratio sum bounds cyclic ratios
ProvedWorkbookSource.base_24798lean-workbooksource-checked
Let a,b,c be positive real numbers. Prove that $\left(\frac{a+b}{c}\right)^2+\left(\frac{b+c}{a}\right)^2+\left(\frac{c+a}{b}\right)^2\geq 4\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)$
Source: InternLM Lean-Workbook, record lean_workbook_24798 (Apache-2.0). Complete source proposition preserved; proof developed independently.
Preamble
import Mathlib open Real Nat
Formal statement
theorem WorkbookSource.base_24798 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b) ^ 2 / c ^ 2 + (b + c) ^ 2 / a ^ 2 + (c + a) ^ 2 / b ^ 2 ≥ 4 * (a / b + b / c + c / a) := by sorry
Source