City Zhautykov 2023 Grade 8 Problem 2
Show that for all positive reals $a, b, c$, $$\frac{a}{{bc}} + \frac{b}{{ac}} + \frac{c}{{ab}} \ge \frac{2}{a} + \frac{2}{b} - \frac{2}{c}.$$ For which $a, b, c$ does this become an equality?
import Mathlib.Data.Real.Basic
def answer : Set (ℝ × ℝ × ℝ) := sorry
theorem solution (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
a / (b * c) + b / (a * c) + c / (a * b) ≥ 2 / a + 2 / b - 2 / c ∧
(a / (b * c) + b / (a * c) + c / (a * b) = 2 / a + 2 / b - 2 / c ↔ (a, b, c) ∈ answer) := sorry
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