Solve the given two equations and select the correct option.
$I.$ $x^{2}-19x+84=0$
$II.$ $y^{2}-25y+156=0$

If $x+y=3$ and $xy=2$,then find the value of $x^3-y^3$.

If $\log_2 x + \log_x 2 = \frac{10}{3} = \log_2 y + \log_y 2$ and $x \neq y$,then $x + y = $

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^2 + (2 - \lambda) x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

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

If $\alpha, \beta, \gamma, \delta$ are the roots of $x^4 - 100x^3 + 2x^2 + 4x + 10 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\delta}$ is equal to: