Find the value of $(a+b+c)^{3}-3(b+c)(c+a)(a+b)$ if $a=5, b=3$ and $c=2$.

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

One root of the equation $3x^2 - 10x + 3 = 0$ is $\frac{1}{3}$. Find the other root.

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $ax^2 + bx + c = 0$,then:

If one root of the equation ${x^2} + px + q = 0$ is $2 + \sqrt{3}$,then the values of $p$ and $q$ are:

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2} = 64$
$II.$ $2y^{2} + 25y + 72 = 0$