Find the value of $a^{2}+b^{2}+c^{2}-2ab+2ac-2bc$,if $a=x+y$,$b=x-y$,and $c=2x-1$.

Solve the given two equations and provide the correct answer from the given options.
$I.$ $391 x^{2} + 1344 x + 1073 = 0$
$II.$ $437 y^{2} + 1074 y + 589 = 0$

Let $p, q, r \in \mathbb{R}$ and $r > p > 0.$ If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta,$ then $|\alpha| + |\beta|$ is:

If the roots of the equation $\frac{\alpha}{x - \alpha} + \frac{\beta}{x - \beta} = 1$ are equal in magnitude but opposite in sign,then $\alpha + \beta = $

In a cubic equation,the coefficient of $x^2$ is zero and the remaining coefficients are real. If one root is $\alpha = 3 + 4i$ and the remaining roots are $\beta$ and $\gamma$,then find the value of $\alpha \beta \gamma$.

Solve the given two equations and select the correct option.
$I.$ $36 x^{2}+47 \sqrt{7} x+105=0$
$II.$ $35 y^{2}+20 \sqrt{3} y+63 \sqrt{2} y+36 \sqrt{6}=0$