Question : If $(a+\frac{1}{a})=–2$, then the value of $a^{1000}+a^{–1000}$ is:

Option 1: $2$

Option 2: $0$

Option 3: $1$

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

Question : If $\text{a}= {\sqrt{2}+1}$ and $\text{b} = {\sqrt{2}–1}$, then the value of $\frac{1}{a+1}+\frac{1}{b+1}$ will be:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

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

Option 1: 1

Option 2: –1

Option 3: 0

Option 4: 2

Question : If $\frac{a}{b}+\frac{b}{a}=-1$ and $a-b=2$, then the value of $a^3-b^3$ is:

Option 1: $0$

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

Option 3: $1$

Option 4: $–1$

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

Option 1: 0

Option 2: 2

Option 3: –2

Option 4: 4