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

Question : If $a^{3}+\frac{1}{a^{3}}=2$, then the value of $\frac{a^{2}+1}{a}$ is ($a$ is a positive number):

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Question : If $(2+\sqrt{3})a=(2-\sqrt{3})b=1$, then the value of $\frac{1}{a}+\frac{1}{b}$ is:

Option 1: $1$

Option 2: $2$

Option 3: $2\sqrt{3}$

Option 4: $4$

Question : If $a+\frac{1}{a-2}=4$, then the value of $(a-2)^{2}+(\frac{1}{a-2})^{2}$ is:

Option 1: 0

Option 2: 2

Option 3: –2

Option 4: 4

Question : If $(a+\frac{1}{a})^{2}=3$, then the value of $a^{18}+a^{12}+a^{6}+1$ is:

Option 1: 3

Option 2: 1

Option 3: 0

Option 4: 2