import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem mathd_algebra_184
  (a b : NNReal)
  (h₀ : 0 < a ∧ 0 < b)
  (h₁ : (a^2) = 6*b)
  (h₂ : (a^2) = 54/b) :
  a = 3 * NNReal.sqrt 2 := by sorry