Solve the given two equations and select the correct answer from the given options:
$I.$ $679 x^{2} - 168 x^{2} = 3066$
$II.$ $\sqrt{144} y^{3} - 9 y^{3} = 1536$

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 the equation $(m - n)x^2 + (n - l)x + l - m = 0$ has equal roots,then $l, m$ and $n$ satisfy:

If the expression $\left( mx - 1 + \frac{1}{x} \right)$ is always non-negative for $x > 0$,then the minimum value of $m$ must be

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is:

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 + bx - c = 0$,then the equation whose roots are $b$ and $c$ is