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

Option 1: $\frac{11}{13}$

Option 2: $\frac{13}{11}$

Option 3: $\frac{16}{9}$

Option 4: $\frac{9}{16}$

Question : If $a=26$ and $b=22$, then the value of $\frac{a^3-b^3}{a^2-b^2}-\frac{3 a b}{a+b}$ is_______.

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

Option 2: $\frac{13}{11}$

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

Option 4: $\frac{11}{13}$

Question : If $(x^2-2x+1)=0$, then the value of $x^4+\frac{1}{x^4}$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If $y+\frac{1}{y}=11$, then the value of $y^3-\frac{1}{y^3}$ is:

Option 1: $345 \sqrt{13}$

Option 2: $360 \sqrt{13}$

Option 3: $352 \sqrt{13}$

Option 4: $368 \sqrt{13}$

Question : If $x = \sqrt[3]{5} + 2$, then the value of $x^3-6x^2+12x-13$ is:

Option 1: $–1$

Option 2: $1$

Option 3: $2$

Option 4: $0$