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

Option 1: $\sqrt[2]{2}$

Option 2: 4

Option 3: 0

Option 4: 2

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

Option 1: $\sqrt{11}$

Option 2: $\sqrt{17}$

Option 3: $\sqrt{15}$

Option 4: $\sqrt{13}$

Question : If $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 1

Option 4: 2

Question : If $x^4+\frac{16}{x^4}=15617, x>0$, then find the value of $x+\frac{2}{x}$.

Option 1: $\sqrt{121}$

Option 2: $\sqrt{129}$

Option 3: $\sqrt{123}$

Option 4: $\sqrt{127}$

Question : If $\frac{3}{(x+2)(2x+1)}=\frac{a}{2x+1}+\frac{b}{x+2}$ is an identity, the value of $b$ is:

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 3