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

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

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

Question : The value of $x$ which satisfies the equation $\frac{x \:+\: a^2 \:+\: 2c^2}{b \:+\: c} + \frac{x \:+\: b^2 \:+\: 2a^2}{c+a} + \frac{x \:+\: c^2 \:+\: 2b^2}{a \:+\: b} = 0$ is:

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