If a 3+ 3a 2+ 9a = 1, then what is the value of a 3+ (3/a)?
28
Divide the given equation by \(a\) (\(a\neq 0\), else \(0=1\)):
\[a^2+3a+9=\tfrac{1}{a}\Rightarrow 3a^2+9a+27=\tfrac{3}{a}\]
Therefore \(a^3+\dfrac{3}{a}=a^3+3a^2+9a+27=1+27=\mathbf{28}\).
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