If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$,then the other roots are

Divide $16$ into $2$ parts such that twice the square of the larger part exceeds the square of the smaller part by $164$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $3216 x^{2} + 3859 x + 481 = 0$
$II.$ $8132 y^{2} - 4839 y + 978 = 0$

If $\cos^4 \theta + \alpha$ and $\sin^4 \theta + \alpha$ are the roots of the equation $x^2 + 2bx + b = 0$,and $\cos^2 \theta + \beta$ and $\sin^2 \theta + \beta$ are the roots of the equation $x^2 + 4x + 2 = 0$,then find the value of $b$.

If $\alpha$ and $\beta$ are the roots of the equation $x^{2}+px+2=0$ and $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ are the roots of the equation $2x^{2}+2qx+1=0$,then $\left(\alpha-\frac{1}{\alpha}\right)\left(\beta-\frac{1}{\beta}\right)\left(\alpha+\frac{1}{\beta}\right)\left(\beta+\frac{1}{\alpha}\right)$ is equal to:

Solve the given two equations and select the correct answer from the given options.
$I.$ $35x^{2} - 53x + 20 = 0$
$II.$ $56y^{2} - 97y + 42 = 0$