Question : Determine the value of $x$, if $x = \frac{(943+864)^2-(943-864)^2}{(1886\times1728)}$.

Option 1: 1

Option 2: 4

Option 3: 79

Option 4: 1789

Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:

Option 1: $\frac{2}{3}$

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

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

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

Question : If $x+\frac{1}{x}=1$, then the value of $\frac{x^2+7x+1}{x^2+11x+1}$:

Option 1: $\frac{3}{4}$

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

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

Option 4: $\frac{1}{4}$

Question : If $2x-\frac{2}{x}=1(x \neq 0)$, then the the value of $(x^3-\frac{1}{x^3})$ is:

Option 1: $\frac{13}{4}$

Option 2: $\frac{13}{8}$

Option 3: $\frac {17}{4}$

Option 4: $\frac{17}{8}$

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

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

Question : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

Option 3: $\frac{7}{2}$

Option 4: $\frac{8}{7}$