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

If $(x^{3}-y^{3}):(x^{2}+xy+y^{2})=5:1$ and $(x^{2}-y^{2}):(x-y)=7:1$,then the ratio $2x:3y$ equals

For what value of $k$ can the quadratic polynomial $3z^{2} + 5z + k$ be factored into a product of real linear factors?

Solve the given two equations and select the correct answer from the given options.
$I.$ $91x^2 + 298x + 187 = 0$
$II.$ $247y^2 + 216y - 391 = 0$

Two candidates attempt to solve the equation $x^2 + px + q = 0$. One starts with a wrong value of $p$ and finds the roots to be $2$ and $6$,and the other starts with a wrong value of $q$ and finds the roots to be $2$ and $-9$. The roots of the original equation are

If $8, 2$ are the roots of ${x^2} + ax + \beta = 0$ and $3, 3$ are the roots of ${x^2} + \alpha x + b = 0$,then the roots of ${x^2} + ax + b = 0$ are