If $x=z=225$ and $y=226$,then find the value of $x^{3}+y^{3}+z^{3}-3xyz$.

The roots of $|x - 2|^2 + |x - 2| - 6 = 0$ are

Solve the given two equations and select the correct answer from the given options.
$I.$ $2x^{2} + x - 1 = 0$
$II.$ $2y^{2} - 3y + 1 = 0$

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - 6x - 2 = 0$. If $a_n = \alpha^n - \beta^n$ for $n \ge 1$,then the value of $\frac{a_{10} - 2a_8}{2a_9}$ is equal to:

$PBA$ and $PDC$ are two secants. $AD$ is the diameter of the circle with center at $O$. $\angle A = 40^{\circ}$,$\angle P = 20^{\circ}$. Find the relationship between Quantity $I$ $(\angle DBC)$ and Quantity $II$ $(\angle ADB)$.

If $\alpha$ and $\beta$ are the roots of the equation $2x^{2} - 3x + 1 = 0$,form an equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.