If $x+y+z=0,$ then find the value of $\frac{(x+y)(y+z)(z+x)}{x y z}$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x = \sqrt{625}$
$II.$ $y = \sqrt{676}$

If $a+b+c=0,$ then find the value of $\frac{1}{b^{2}+c^{2}-a^{2}}+\frac{1}{c^{2}+a^{2}-b^{2}}+\frac{1}{a^{2}+b^{2}-c^{2}}.$

If $x$ is real,the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

Solve the given two equations and select the correct option.
$I.$ $676 x^{2}-1=0$
$II.$ $y=\frac{1}{\sqrt[3]{13824}}$

If the roots of the equation $x^2 + x + 1 = 0$ are $\alpha$ and $\beta$,and the roots of the equation $x^2 + px + q = 0$ are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$,then $p$ is equal to: