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 $a+\frac{1}{a}=1$, 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 $(x+\frac{1}{x})^{2}=3$, then the value of $(x^{3}+\frac{1}{x^{3}})$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

Question : If $\frac{3–5x}{2x}+\frac{3–5y}{2y}+\frac{3–5z}{2z}=0$, the value of $\frac{2}{x}+\frac{2}{y}+\frac{2}{z}$ is:

Option 1: 20

Option 2: 5

Option 3: 10

Option 4: 15

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

Option 1: 1

Option 2: 0

Option 3: –1

Option 4: 2