import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12a_2002_p13
  (a b : ℝ)
  (h₀ : 0 < a ∧ 0 < b)
  (h₁ : a ≠ b)
  (h₂ : abs (a - 1/a) = 1)
  (h₃ : abs (b - 1/b) = 1) :
  a + b = Real.sqrt 5 := by sorry