Question : What is the simplified value of $(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x-\frac{1}{x})(x^{16}+\frac{1}{x^{16}})(x+\frac{1}{x})(x^{4}+\frac{1}{x^{4}})?$

Option 1: $(x^{64}+\frac{1}{x^{64}})$

Option 2: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$

Option 3: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x+\frac{1}{x})}$

Option 4: $\frac{(x^{32}-\frac{1}{x^{32}})}{(x+\frac{1}{x})}$

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

Option 1: 4

Option 2: 5

Option 3: 6

Option 4: 8

Question : If $x^4+x^{-4}=194, x>0$, then the value of $x+\frac{1}{x}$ is:

Option 1: 14

Option 2: 6

Option 3: 4

Option 4: 8

Question : What is the value of $\frac{x^2-x-6}{x^2+x-12}÷\frac{x^2+5x+6}{x^2+7x+12}$?

Option 1: $1$

Option 2: $\frac{(x-3)}{(x+3)}$

Option 3: $\frac{(x+4)}{(x-3)}$

Option 4: $\frac{(x-3)}{(x+4)}$

Question : If $x$⁴ + $x$ ^-4 = 194, x > 0, then what is the value of $x+\frac{1}{x}+2$?

Option 1: 8

Option 2: 14

Option 3: 6

Option 4: 4