Solve the given two equations and select the correct answer from the given options.
$I. 3x^2 - 4x - 32 = 0$
$II. 2y^2 - 17y + 36 = 0$

Solve the given two equations and select the correct option.
$I.$ $\frac{x}{x-11} + \frac{x-11}{x} = 7$
$II.$ $\frac{4y}{4y-13} + \frac{4y-13}{4y} = 9$

With respect to the roots of $x^{2}-x-2=0$,we can say that

If the roots of the equation $x^2 + px + q = 0$ are $\alpha$ and $\beta$,and the roots of the equation $x^2 - xr + s = 0$ are $\alpha^4$ and $\beta^4$,then the roots of the equation $x^2 - 4qx + 2q^2 - r = 0$ will be:

If $x = 2^{1/3} - 2^{-1/3}$,find the value of $2x^3 + 6x$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{3} \times 13 = x^{2} \times 247$
$II.$ $y^{1 / 3} \times 14 = 294 \div y^{2 / 3}$