Let a and b be positive real numbers. If a, A₁, A₂, b are in arithmetic progression, a, G₁, G₂, b are in geometric progression and a, H₁, H₂, b are in harmonic progression, G₁ G₂ A₁ + A₂ show that (2a + b)(a + 2b) 9ab H₁ + H₂ H₂H₂ 2 = =

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