Find the value of $x^{3}+y^{3}+z^{3}-3xyz$ when $x=89, y=87, z=84$.

If $x = a^{1/2} + a^{-1/2}$ and $y = a^{1/2} - a^{-1/2}$,then find the value of $(x^4 - x^2 y^2 - 1) + (y^4 - x^2 y^2 + 1)$.

If $\alpha, \beta$ are the roots of the equation $x^{2}-5x+6=0$,construct a quadratic equation whose roots are $\frac{1}{\alpha}, \frac{1}{\beta}$.

Babu starts from his house at a certain time with a certain speed to pick up his girlfriend from the office at $5:00 \, PM$. One day,his girlfriend left the office at $3:00 \, PM$ and started walking home at a speed of $40 \, km/h$. She met Babu on the way,who had left his home at his usual time. They reached home $40 \, min$ earlier than their usual time. If Quantity $I$ is the speed of Babu and Quantity $II$ is $120 \, km/h$,compare the two quantities.

Solve the given two equations and select the correct option.
$I.$ $\frac{18}{x^2} + \frac{6}{x} - \frac{12}{x^2} = \frac{8}{x^2}$
$II.$ $y^3 + 9.68 + 5.64 = 16.95$

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{12 \times 4}{x^{4/7}} - \frac{3 \times 4}{x^{4/7}} = x^{10/7}$
$II.$ $y^3 + 783 = 999$