Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?

Option 1: $\frac{3\sqrt{3}}{5}$

Option 2: $\frac{3\sqrt{15}}{5}$

Option 3: $\frac{3\sqrt{15}}{8}$

Option 4: $\frac{3\sqrt{5}}{8}$

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$; then what is the value of $x+\frac{1}{x}$?

Option 1: $2$

Option 2: $\frac{\sqrt{15}}{2}$

Option 3: $\sqrt{5}$

Option 4: $\sqrt{3}$

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

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : If $x + \frac{1}{x} = \sqrt{3}$, then the value of $x^{18} + x^{12} + x^{6} + 1$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If for a non-zero $x$, $3x^{2}+5x+3=0,$ then the value of $x^{3}+\frac{1}{x^{3}}$ is:

Option 1: $\frac{10}{27}$

Option 2: $-\frac{10}{27}$

Option 3: $\frac{2}{3}$

Option 4: $-\frac{2}{3}$