Q. Consider an equation $lo g_{2} (α^{6} - 16 α^{3} + 66) + 4 β^{4} - 8 β^{2} + 13 + ∣ ∣ [\frac{γ}{3} - 2] ∣ ∣ = 4$ and $m, n$ and $r$ are the number of integral values of $α, β$ and $γ$ respectively which satisfy the above equation.
The number of ordered triplets $(α, β, γ)$ is

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2

Solution: