Question : If $\small a^{3}+3a^{2}+9a=1$, then what is the value of $a^{3}+\frac{3}{a}$?
Option 1: 31
Option 2: 26
Option 3: 28
Option 4: 24
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Correct Answer: 28
Solution :
$a^{3}+3a^{2}+9a=1$ .......(i)
Multiply the equation by $\frac{3}{a}$ both sides,
⇒ $3a^{2}+9a+27=\frac{3}{a}$ ......(ii)
Subtracting (ii) from (i),
⇒ $a^{3}-27=1-\frac{3}{a}$
$\therefore a^{3}+\frac{3}{a}=28$
Hence, the correct answer is 28.
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