Question : If $x+\frac{1}{x}=9$, find $x^4+\frac{1}{x^4}$.

Option 1: 5431

Option 2: 6561

Option 3: 6156

Option 4: 6239

Question : If $2 x^2-7 x+5=0$, then what is the value of $x^2+\frac{25}{4 x^2} ?$

Option 1: $5 \frac{1}{2}$

Option 2: $7 \frac{1}{4}$

Option 3: $9 \frac{1}{2}$

Option 4: $9 \frac{3}{4}$

Question : If $(\frac{5}{9}\times x)-(\frac{2}{5}\times \frac{9}{4})=-\frac{4}{5}$, then find $x$.

Option 1: 0.18

Option 2: 0.12

Option 3: 2

Option 4: 0.54

Question : If $x+\frac{1}{x}=6$, then find the value of $\frac{3 x}{2 x^2-5 x+2}$.

Option 1: $1$

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

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

Option 4: $0$

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: $\frac{1}{4}$