If $x+\frac{1}{x}=2,$ then the value of $x^{12}-\frac{1}{x^{12}}$ is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $81x^2 - 9x - 2 = 0$
$II.$ $56y^2 - 13y - 3 = 0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-7x+12=0$
$II.$ $y^{2}+y-12=0$

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 - x - 1 = 0$,then the equation whose roots are $\frac{1}{\beta + \gamma}, \frac{1}{\gamma + \alpha}, \frac{1}{\alpha + \beta}$ is:

The roots of the equation ${x^4} - 8{x^2} - 9 = 0$ are

Solve the given two equations and select the correct option.
$I.$ $9x^{2} - 114x + 361 = 0$
$II.$ $y^{2} = 36$